As a result of recent payments to the federal government made by large oil companies accused of illegally jacking up petroleum prices, Northern Virginia motorists now can have their car problems diagnosed free of charge.

The system was developed to compensate those who may have paid higher prices at local gas stations.

The Car Chek program, using a talking computer with more cable attachments than an octopus has tentacles, began testing cars two weeks ago at Northern Virginia Community College's Alexandria and Manassas campuses.

The computer, a $25,000 machine called the Interrogator, runs a car through 103 tests in 45 minutes, checking everything from starter, battery and alternator to carburetor, air filter and fuel injector to valves, rings and catalytic converter. A comparable car diagnosis would cost about $40 at a commercial garage.

The car testing program, recently set up at 19 community colleges across Virginia, is financed by the U.S. Department of Energy's Petroleum Violation Escrow Fund. Virginia's $600,000 portion of the fund came from Amoco Corp.'s $100 million out-of-court settlement with the Department of Energy in 1980. Amoco allegedly violated federal oil price controls between 1973 and 1979, said Tom Mann of the Department of Energy.

"The administration [of the U.S. Department of Energy] decided that the money should be distributed according to the use of Amoco's fuel during the period when price controls were allegedly violated," said Temple Bayliss, director of the energy division of Virginia's Department of Mines, Minerals and Energy.

"The program was to have a direct benefit for users of motor gasoline. They were the guys that were overcharged," said Bayliss.

Although petroleum price controls were lifted in 1981, settlements between the federal government and oil companies still are being worked out in court. This could provide even more money to benefit oil consumers, said Paul Friedt, an instructor in automotive technology at the Alexandria campus.

The state has asked the Alexandria campus to check 932 cars over the next two years. Already there is a backlog of cars signed up for tests, but about 70 more cars can be tested in the next two months, said Patrick Devlin, an assistant professor in the Alexandria campus' automotive engineering department, who heads the Car Chek program. After the two years, the college will own the Interrogator and train students on it, Devlin said.

"Car Clinic," a one-hour slide program on fuel economy, also is financed by the Petroleum Violation Escrow Fund. The program is free and can be taken to groups of 20 people or more, Devlin said.

Although the computer can be programmed to check cars that were built before World War II, the Interrogator cannot check cars or trucks with diesel engines and hot rods, noted Devlin.

"It the electrical wiring in hot rods throws the computer out of whack," Friedt said.

Those interested in the Car Chek or Car Clinic can make an appointment by calling Alexandria's Automotive, Engineering and Public Services department at 845-6230 between 9 a.m. and 4 p.m., Monday through Friday.