WHEN REDSKINS like Joe Theismann are injured, the ambulance speeds them across the river to Arlington Hospital, though a perfectly good trauma center stands just a long city block away. It is part of D.C. General, Washington's only public hospital, almost half of whose $102 million budget is picked up by those ardent Redskin fans, the city's taxpayers.

But the Redskins aren't the only ones who pass D.C. General by. In the eight years I served as a member of the hospital's governing board, people invariably had two questions to ask me. One was: Where IS D.C. General? (Answer: next door to RFK Stadium, on the Orange and Blue Metro lines). The other: "Did the hospital ever get its accreditation back?" (Answer: Yes, in 1978, a year after the commission first took over, after a 3 1/2-year gap).

In cities like Atlanta or Dallas (where a fatally wounded President Kennedy was rushed to Parkland, a public hospital) schoolteachers or businessmen or secretaries are aware of their public hospital and can be familiar with its problems. But in the nation's capital, D.C. General -- required by law to accept all comers regardless of ability to pay, and thus the city's hospital of last resort -- remains a shabby, shadowy presence.

It is vaguely known as a refuge for poor blacks who live in the surrounding Northeast and Southeast neighborhoods and who cannot afford to go to the city's more prestigious hospitals. It is somewhere "out there" to most people, an object of derision when things seem to go wrong, and definitely someone else's business.

D.C. General should matter to all Washingtonians, not only as a matter of conscience and economics, but as a matter of self-interest. In fact, the income-tax payers of the District should get ready to shell out an extra $188 apiece -- the price of a good- looking dress or a stereo component -- to raise the $60 million necessary immediately to replace D.C. General's rambling 25-building plant with a smaller but far more efficient one-building modern hospital.

We have no real alternative but to maintain D.C. General. The other hospitals in the city don't want the public hospital to close. They have all the uninsured patients they can handle. And they don't have the space to handle D.C. General's huge load of outpatient visits -- 70 percent of them uninsured.

What's more, though the more prestigious hospitals don't talk openly about it, they worry about a large influx of uninsured, terribly expensive patients -- like AIDS victims (who, a Center for Disease Control study of 9,000 found, used 1.5 million hospital days at an average cost of $830 a day). Such high costs, along with a public hospital clientele which includes penniless alcoholics or jail inmates along with the more ordinary sick, might drive 90,000 suburban patients out of our hospitals with fancier addresses, to seek care in exurbia.

The mayor of this city certainly does not want its public hospital to close. In making his commitment, Marion Barry is responding to his majority black constituency as well as to his conscience. D.C. General, a large, primarily black institution, reaches out to a service area that is almost 90 percent black, with a large percentage of poor residents.

For our own sake as well as that of our friends, families and fellow human beings who have no other choice, the residents of the District should help D.C. General become what its mission statement says it wants to be -- "a health care center to which anyone might want to turn."

D.C. General runs the metropolitan area's busiest emergency room. Any of us could end up there at any time -- violently battered, bruised or raped -- and be in such bad shape we could not be transferred to another hospital even if we wanted to be.

Right now, D.C. General is not a hospital to which "anyone might want to turn." It is true that its 2,300 staff members do take care of the 14,400 people admitted to the hospital annually and the 204,400 treated in its emergency room and outpatient clinics in a professional-enough manner that one patient recently responded in a survey, "It's much better than most people in the community say." In fact, a doctor new to the scene added, after looking at the comparatively new ob-gyn building and the care it gives: "Why, this is a nice place."

Others have been impressed with the hospital's trauma center, its geriatric and adolescent units and its neonatal nursery (including a roomful of tiny drug-affected babies of drug-addicted mothers.)

What's more, the mayor has finally given the hospital the go-ahead to build a desperately needed, $14 million building that would put the emergency room, most outpatient clinics and all intensive care and critical care facilities under one roof adjacent to the central "core" buildings. Six years in the planning and approved by numerous panels and governmental bodies, the new space will help correct some serious deficiencies -- like six-hour emergency-room waits or critical care that has to be attempted in cramped cubicles without enough space for staff or high-tech monitoring equipment.

If the doctors can get their act together, this new facility will allow them to set up some sort of group practice wherein they could both do better financially and patients could see their "own doctor" instead of interns or residents they probably don't know.

But this $14 million won't be enough to keep D.C. General up to conscionable standards for very long. The public hospital will need several million more dollars in operating funds each year just to stay where it is, much less improve its surgery and physical and occupational therapy departments, as it wants to do. And it must begin to plan now to spend that $60 million to replace its rambling 25-building plant with a smaller one-building modern hospital.

Unless such a new streamlined hospital is built, our "hospital of last resort" will be k with a maze of sprawling, aging buildings, some connected by dank, dark tunnels and cursed with endless corridors and creaking elevators, where security is hard to maintain and medicine, machinery, food and laundry are difficult to carry back and forth.

Unless such a new hospital is built, patients, many of whom are beset with a multitude of serious illnesses (the result of a lifetime of poverty and neglect), will suffer in crowded, poorly ventilated and poorly designed quarters (usually four to a room), whose pipes and electric wires are in constant need of noisy repair.

Most of today's D.C. General is undeniably dowdy. The corridors are often noisy and the bathrooms are sometimes unclean. If patients don't complain, perhaps it's because they feel it's their hospital -- or they are grateful for their treatment. One lady recovering nicely from a routine gall bladder operation in a single room (which, like all patient rooms, had its own television set and telephone), excused the few roaches she had seen crawling the wall: "Well, it's an old building."

Administrators fight a losing battle against these frayed quarters, repaired and renovated to the point of exhaustion. As they do so, they are frustrated by the knowledge that their efforts are not cost-effective. It would be cheaper in the long run to invest in a replacement hospital rather than continue to pour some $5 million a year into an elephantine structure which will be obsolete in just six more years.

In fact, planners estimate that the cost savings -- on energy, on maintenance, on housekeeping and staff -- from a well-designed, compact new hospital would be more than $50 million over a 10-year period. In other words, a replacement hospital would almost pay for itself in a decade.

Cost-effectiveness, compassion and self-interest are not the only reasons Washington should make an extra effort and find some extra funds for D.C. General. The public hospital is doing an increasingly important job for the whole city in a dramatically changing health care scene: accepting patients other hospitals cannot or do not want to take care of.

What's happening is that the other 12 hospitals scattered about the city are transferring to D.C. General 5 1/2 times more patients who cannot foot their own bills than they did in 1981 (930 this year instead of 169). Some call this "dumping." D.C. General politely calls it "transferring" because in all but a tiny percentage of cases, the other hospitals adhere to D.C. General's guidelines. For instance, they don't subject unstable accident victims or women in the midst of difficult labor to the shaking of an ambulance ride.

There are about 100,000 people in the capital city without health insurance, accordig to the D.C. Hospital Association. If they are like their some 30 million counterparts nationwide, they are by no means all Dickensian street people; three-quarters are workers or related to workers. This means they may be "respectable" folks -- out of work, or between jobs, or in small businesses which lack health benefits -- too young for Medicare or not lucky enough to fit into one of the strict government Medicaid categories.

The private hospitals are not turning their backs on these people because they are mean-hearted. Spurred on by both federal and state obligations, they still handle $96 million worth of uncompensated care. Nor are they doing it because they don't have extra beds; citywide, their beds are only 74 percent full. They are doing it because they are caught in a new kind of financial crunch.

Where does all this leave D.C. General? Precariously perched on all the city's unpaid bills. It has more admissions than it used to have, but most are dumped indigents. Like its sister hospitals, it has extra beds. It also has a staff of doctors earning an average of $60,000 a year, who have formed a union and will demand higher wages. D.C. General also has been deeply affected by stricter reimbursement policies and has had to cut lengths of stay (from an average of 11.27 days in 1981 to 8.7 today). Unlike the other hospitals, though, D.C. General lacks any real base of private patients.

D.C. General commands a loyal following in its Southeast and Northeast neighborhoods, who bring it everything from bee stings to heart attacks. From anywhere in the city, it gets occasional babies born on the toilet without prenatal care. And it receives people with many problems, like a man who was blind in both eyes, had high blood pressure, degenerative joint disease of the spine and right sided weakness (listed on a form as having "no special needs").

D.C. General knows it needs to attract a "better mix" of patients -- customers with insurance as well as those without it -- if it is to carry out its mission of caring for everyone, regardless of ability to pay, and still keep costs down and survive. Sadly, it is losing what ability it has had to compete for insurance cardholders with other increasingly aggressive hospitals (particularly with the Washington Hospital Center, which now owns Capitol Hill Hospital and plans to open outpatient clinics nearby that could skim off local paying patients) and new types of medical purveyors, like shopping mall medical walk-in centers.

D.C. General will try to meet this competition with a professional marketing program, aimed at insured customers. The new ambulatory-critical care building, too, will help D.C. General compete effectively for patients who are ambulatory (walking around). And when they can't walk around any longer, it can treat them in its own beds (which are any hospital's chief source of revenue).

But if they are not replaced, the old core buildings, with their shabby image, will hamper such efforts. Right now, moreover, it seems to take forever to replace even obsolete equipment. It took a year and a half to get the funds to replace cardiac catherization and radiology equipment (such as a machine bought in 1964 that performs mammograms as well as general X-rays of the chest, spine, arms, legs and pelvis) which the medical director has testified is unreliable and technically obsolete.

The truth of the matter is that, in to-day's health care era, it is getting less and less possible for D.C. General to limp along as an adequate, uncompetitive hospital -- one that lacks not just amenities like steak and champagne dinners for new parents, but comfortable and well-ventilated space and well-maintained, state-of-the-art equipment.

Patients, even "poor" (but insured) patients, won't come to it. Doctors won't practice there without up-to-date tools (D.C. General had trouble engaging the services of a neurosurgeon before it finally got a CAT scan). The host of accreditory and regulatory bodies which monitor hospitals nowadays, led by the Joint Commission on Accreditation of Hospitals, won't allow substandard facilities.

The bottom line is that closing a public hospital does not necessarily work out. Philadelphia, which has more than twice as many hospitals as Washington, closed its public general hospital after Medicare and Medicaid gave patients options to go elsewhere in the 1970s. Now that city's health commissioner, Dr. Stuart Shapiro, says it was a "terrible mistake" to do so without adequate planning; needy patients are slipping through the cracks, without a place whose special mission is to care for them.

Washington has such a place in D.C. General, which underpins the whole city's health care system. With a new ambulatory-critical care building, it is on its way to becoming a health care center to which anyone might want to turn. It should be given the wherewithal, including the $60 million it needs for a replacement hospital, which will allow it to reach that goal. Any other course would be fraught with danger -- fiscal as well as medical.

This capital does not want to be a city whose public hospital just gets by, pouring good money after bad into an ineffective, barely satisfactory set of buildings. Nor does it want to be a city where you can suffer, and die, without adequate hospital care, because you are unlucky enough not to be able to pay your medical bills.