the car will turn over but wont stay running and sometime backfires as it dies

i have a 1982 cadillac eldorado biarrittz with a ht4100 motor. the original problem was the car wouldnt start. i started messing with the distributor because it sounded as if it was a timing issue. i seem to have had the timing issue fixed because the car will turn over and run for about 5 to 7 seconds but then cuts off. if i give it gas it dies faster and sometimes backfires out of the throttle body. i have replaced all of my plugs and wires and distributor cap. i have check the fuel pump and it is working properly and the injectors are spitting gas out properly. i have checked all the fuses and relays. what is the next step in getting my car running.