mine did that when my fuel pump relay went out..but I did replace both. first replaced the fuel pump and it didnt run then I replaced the relay and it ran fine.
mine died on me and it would start then run then when it was shut off it wouldnt start. had it towed home and started it the next day. then it wouldnt start again.
if your car is like mine you can jump 2 pins on the relay and see if it will start.
mine is a 1982 380 SEC I have the CD for that car and can send you some info on jumping the relay if you need it
1982 380 SEC