car starts but stops immediately; please help

Mine is 95 SL1. Last week I started my car and while backing up, it stopped suddenly. I started it again. It started but stopped again after driving for 30 secs. I pushed it back home.

It used to run very good. The lights and radio are working, so no battery problem i guess. When I try to start, it sounds as if it is about to start but stops immediately. What parts should I check.

If it turns over fine I would start by checking fuel pressure. It sounds like a pump to me just be sure to check fuses, relays(fuse panel inside on pass. side of console) and filter. You should be able to hear the pump run for about 10 sec. upon turning the key to the run position. The pump should hold 40 psi after four cycles turn key on wait 10s turn off 15s turn on 10s. ...