PETERSBURG, VA., SEPT. 8 -- The spindly 7-year-old, her twisted body cradled in the arms of a hospital volunteer, hummed softly, oblivious to the dignitaries touring the Southside Virginia Training Center here today.

"When I came here 30 years ago, we didn't know it was possible to get a response" from such a profoundly retarded patient, said Conroy Johnson, director of nursing services at the 762-bed facility for the severely retarded and multiply handicapped.

Now, thanks in part to medical advances -- and the dedication of volunteers such as Alamena Jones, who in 14 years here has taught more than one previously speechless patient to hum or sing -- "these people are getting a level of care we only dreamed about," Johnson said.

Needs remain, however, and during a four-day tour of state facilities -- mental hospitals, prisons and colleges -- that began today, Gov. Gerald L. Baliles, his Cabinet secretaries and key state legislators are getting a firsthand look at some of the nearly $1 billion in construction projects that state agencies are requesting be financed in Virginia's 1988-90 budget, which Baliles will present to the legislature in January.

Virginia is one of the few states that determines construction projects partly on the basis of an on-site inspection by its legislative and executive leaders. Far from being a barnstorming political tour, the inspections are a no-nonsense look at the underbelly of state facilities.

At Southside, administrators are requesting $1.4 million in the next biennial budget for repairs to the center's heating and air-conditioning system. Making a pitch today for a new system, one Southside official said that because many of the residents suffer from upper respiratory ailments, "we have to use humidifiers and air conditioners at the same time. And today -- and this was not planned -- the air conditioning is broken."

"There goes the surplus," said Del. Alson H. Smith Jr. (D-Winchester), alluding to the $154 million budget surplus Baliles announced last month.

Like nearly all in the 40-member delegation, Smith was grim and serious as he toured the institution, where, according to nurse Jeannie Laine, only two of the 40 patients in her building can feed themselves.

Del. Vincent F. Callahan Jr. (R-Fairfax), who first toured Southside in the early 1970s, recalled "it was a smelly hellhole, where patients were warehoused."

Despite the overpowering scene here, Secretary of Human Resources Eva S. Teig said the major needs in mental health are community-based facilities. Two weeks ago the board that oversees mental health programs in Virginia endorsed a proposal to add $140 million to community-based health initiatives in the state by 1990. Such programs are now funded at $160 million.

Del. Marian Van Landingham (D-Alexandria) noted that there is a waiting list for admission to the Northern Virginia Mental Health Institute in Fairfax. A lack of halfway houses accounts for many of the homeless, she said, adding, "You can see them walking around Old Town."

Advocacy groups are hoping to persuade Baliles to declare 1988 the year of mental health, as previous years have targeted trade, transportation and education.

Sen. Joseph V. Gartlan Jr. (D-Fairfax), a member of the Senate Finance Committee, said he and Del. Franklin M. Slayton (D-South Boston) urged Baliles at the end of this year's legislative session to adopt the cause.

"He was a little reluctant to make a big push without indications that the powers that be in the legislature would respond favorably," Gartlan said. Since then, he added, "there have been very solid indications" that legislators, led by House Appropriations Committee Chairman Dorothy S. McDiarmid (D-Fairfax), are ready to support such an initiative.

But Baliles repeated today what he told the General Assembly's money committees when he revealed the surplus: "Don't rush to judgment." He wants them to weigh all the requests before deciding where and how much money to spend.

"Over the years the various issues balance out," McDiarmid said. "I have the feeling this time we're leaning toward the human services areas."

Nursing supervisor Johnson said that when he began working at Southside, few patients lived to adulthood, but that in the three decades since, the average patient's lifespan has nearly doubled, with the oldest one now 45.

Asked if he considered that progress, Johnson said: "It depends on where you are. If you're worried about costs, it's not good." He added: "These people have a right to life, for as long as we can provide it."