Ever since Mae Davis and her three children moved here from Gary, Ind., five years ago, they have suffered one calamity after another. It's bad enough that Davis fell ill with cancer and had to undergo three operations, and bad enough that the children's asthma seems to be getting worse.

But this winter their troubles are verging on ridiculous extremes. Last week Davis received a notice from Pepco of the utility's intent to cut off her electricity. The next night, as the temperature outside fell to 20 degrees, her furnace exploded and the gas company told her it would cost $2,400 for a new one.

Finally, after receiving three space heaters and emergency money from Prince George's County to stop the power cutoff, Davis returned to her Capitol Heights home only to find three police cars outside with red lights flashing. There had been a break-in while she was away.

"I don't feel anything anymore. Just numb," Davis said, slumping on her porch with eyes full of tears, as police dogs loped inside her house to sniff out a suspect. "I wish this winter would hurry up and go away."

Mae Davis' story is just one of thousands of luckless tales needy people have brought to the Prince George's County Energy Assistance Office in Hyattsville since the start of winter.

A branch of the federally funded Maryland Energy Assistance Program--which is entirely supported by the windfall-profits tax on oil companies--the office ministers to the poor by paying limited portions of their fuel bills, providing money for space heaters, and helping to insulate houses.

"When people are hurting in winter we're usually the first to hear their cry," said R. Hal Silvers, director of the Prince George's office. "When it's cold outside it's often a disaster just being poor."

"A sad tale's best for winter," Shakespeare once wrote. In the suburbs, despite the season's unusually mild weather--8 degrees above normal in December, and 3 degrees this month--sad tales seem to abound.

At the Kentland Volunteer Firehouse in Landover, for instance, firefighters are still talking about a blaze they battled last month that started when an irate unemployed husband poured gasoline over a pair of gloves someone had given his wife. He lit a match and burned his house down. The man perished in the fire, but his wife escaped.

In College Park, meanwhile, merchants remember a tramp who spent several nights last week buried beneath cardboard boxes under a Rte. 1 overpass. He said his name was Phil Kuech, that he was 40 years old, and hitchhiking his way south "with the birds" from New York to a job in Tampa, Fla. He sojourned in the Maryland suburbs for a full week, and when last seen he was still trying to hitch a ride.

And in the basement of the Seat Pleasant police station, officials are saying cold weather crimes have once again come to the fore. "When it's cold you find people shoplifting sweaters and overcoats instead of bikinis," said Lawrence Thorner, a Prince George's County District Court commissioner.

"I had an elderly couple come in a while ago complaining about getting fleeced by a guy going around selling cut-rate fuel . . . Some things stay the same from year to year," he said.

But no place seems to attract so many disquieting stories of the season as the energy assistance office in Hyattsville, where families gather each day to ask for help. The office is buried in the cinderblock basement of the county police station on Rhode Island Avenue, down the hall from a jail.

This winter, aid applicants have tumbled into that office, and its counterpart in Montgomery County, at a record pace. Since opening its doors Nov. 15 at the start of the cold weather season, the Prince George's office has processed 2,940 cases, up 42 percent over the same period last year, while Montgomery has helped 1,520 households, a rise of nearly 20 percent.

Statewide, the number of poor people requesting fuel aid has gone up 14.5 percent. Stephen Minnich, director of the $32 million Maryland program, said he expects fuel assistance offices to handle more than 80,000 cases statewide by the end of the season on April 1, an increase of 13,000 over last year.

The Maryland energy assistance office and its counterparts in D.C. and Virginia are entirely supported by grants from the federal government's Low Income Home Energy Assistance Program, which is run by the Department of Health and Human Services. This year the federal government received $1.3 billion in oil company windfall profit taxes to allocate to the states.

D.C. and suburban Virginia officials, like Maryland's, report a steep increase in fuel aid applicants. Chuck Clinton, director of the D.C. office, said 150 to 200 residents a day have asked for help, and that he expects the total to "considerably exceed" last year's 12,000 figure.

Arlington County energy assistance officials said they have already processed 912 cases, only 7 households short of last year's total number. And in Fairfax County, officials said they have spent $363,331 on fuel assistance to the poor, a jump of 32 percent over last year.

Officials attribute the increase in applicants to fuel rate increases and unemployment. "Around here it's clearly tied to the economy," said Mary Bladen, director of the Montgomery office. "We're just seeing more and more people who have been laid off from their jobs . . . "

Prince George's director Silvers added, "It may seem warmer than usual outside, but a lot of people are suffering."

On a recent weekday several families with small children waited for help in the Hyattsville office, several yards down the hall from another group of people hoping to bail friends and relatives out of jail.

"I'm only gettin' $500 a month income," said Marie Carroll, an unemployed Suitland mother of five children living on welfare. "I gotta pay the mortgage out of that, plus food, heat, electricity . . . There's just not enough to go around." She shushed one of her children, then pulled out a gas bill from her purse. "Look at this! It's gone up from $70 to $98 a month since last year . . . If I couldn't get any help from this place, I'd probably have to go without heat."

Which is exactly what many indigent people in the Maryland suburbs did before the energy assistance office was opened four years ago, according to Silvers, a stout, mustachioed man. "There were a lot of cases where people just set fires in their living rooms to keep warm. Even now I'm finding people who are too proud to come here for help.

"A couple of weeks ago an elderly woman came in with tears in her eyes, saying, 'Oh, Mr. Silvers, I've never accepted charity before.' She needed something like $65 for the oil man. Our funding comes from the windfall profit tax, so I said to her, 'Look, ma'am, you want me to just give this money back to Exxon? You think they could use it more than you?'

"It took about an hour," Silvers went on, "but I finally persuaded her to let me pay for the oil."

Of all the troubles people bring to Hyattsville, however, none seem as startling as those of Mae Davis. She was trying to scrape up enough money to make a suitable payment to Pepco on her $499.51 electricity bill when her gas furnace suddenly exploded last week. "I just sat down on my basement steps and cried. I mean, why did all this have to happen to me?"

As a U.S. Health and Human Services personnel clerk, Davis, 35, a single parent, earned $15,000 a year until a series of operations last year forced her to leave the job, she said. Having exhausted all of her sick leave benefits, she said she is now on leave without pay from her job.

Davis shares the Larchmont Avenue home with her three children, De Juan Davis, 14, Michael Davis, 13, and Marion Dawson, 9, and her niece's two children whom she is trying to adopt, Jerilyne Steele, 4, and Richard Steele, 2.

For two nights after the furnace exploded, Davis and the five children slept on the kitchen floor next to a gas stove that still worked. "It's real bad on the kids," she said. "A winter doesn't go by without at least one of them ending up in the hospital with an asthma attack."

Finally, Davis asked around the neighborhood for advice and was directed to the energy assistance office, where a case worker paid Pepco enough money, $275, to postpone the electricity cutoff.

When Davis returned home with the space heaters she found the police cars, along with a neighbor, Gene Crowell, who said he saw someone kick in her front door. "I called the police and got my .44 magnum," Crowell said, "but by the time I got there the guy was gone."

No suspects were captured in the incident and Davis said nothing was taken.

Yesterday, Davis said she and the children were still walking around the house and sleeping with their coats on because "the space heaters aren't giving out enough heat."

She said she had been doing quite a lot of thinking and has decided to retire from the federal government. "That way," she said, "I'll be able to get $4,000 in retirement money to pay for a new furnace. The rest I'll use to try to fix up the house. Then maybe I'll sell it and move into an apartment.

"When I left Indiana I wanted to get away from all that misery. You know, nobody's working back there and it's always so cold. I figured I'd find a job here to make things better for the kids. But I tell you, I've never seen a winter like this."