I copied this from another thread awhile back, sorry I can't give the original poster credit. Maybe it will help:
"IF the oil pressure sending unit is unplugged and IF, the fuel pump relay is faulty, then the pump will not run, and no start. The oil pressure sending unit and fuel pump relay are in parallel, which is why the fuel pump relay can be faulty or removed and the car will still start and run as soon as oil pressure comes up during cranking. But one of them needs to work."
John