The Metro board, trying to stop a serious decline in Metrorail reliability, voted yesterday to seek federal aid for a $44 million program to replace or repair motors, brakes and other troublesome parts in the fleet's 300 cars.

But Urban Mass Transportation Administration deputy chief Charles Gargano cast doubt on Metro's chances for a grant from the agency's modernization fund. Metro is counting on getting $35 million from the fund to cover 80 percent of the three-year program.

Current policy, Gargano said, is to deny the modernization grants to new rail systems such as Metro that were built largely with federal money in the first place. UMTA feels it should not pay twice.

If the request is denied, the board probably would face the politically difficult choice of diverting federal construction funds, already in short supply, or persuading area governments, already heavily burdened by subsidies, to finance the plan themselves.

Yesterday's vote followed a stormy board meeting last week at which Virginia board members blocked the motion on the grounds that the budget committee had not considered it and area governments might be hit by enormous new costs if the federal money was not available.

Yesterday, after discussion by the budget committee, Virginia members voted for the plan. If modernization grants are turned down, the board will have to reconsider the plan. But member Joseph Alexander of Virginia said he feels Metro is committed to find the money one way or another. "The system needs this program, no question about it," he said.

The resolution was further evidence of a consensus on the board that Metro has been preoccupied with building the costly rail system and has let service deteriorate.

The program would devote $10 million to replace failing parts in motors that drive the cars. About $7 million would go for new brakes. The rest of the funds would go to such things as air conditioner compressor motors, electronic boxes that assist in controlling power flow in cars, and interior panels and runners under the doors.

In other action yesterday:

* The board's budget committee backed a proposal to buy 16 surplus rail cars from the Massachusetts Bay Transportation Authority in Boston.

Metro officials hope the purchase would improve service by freeing up four passenger cars now used to haul trash, farecard cash and equipment and crews. The Boston cars would cost about $1.7 million, according to Metro.

* General Manager Richard S. Page presented preliminary working numbers for the draft fiscal 1984 operating budget. Holding service at current levels would raise costs by about 15 percent to $389 million, he said, and subsidies by 25 percent to $221 million.

Opening new Blue and Yellow line track that is nearing completion and improving general levels of service would raise costs by 19 percent to $405 million and subsidies to $235 million, a 33 percent increase over this year's levels. The numbers do not include debt service. Both plans assume fares would rise this January.