You wont hear the fuel pump running with just the ignition on - it only runs when you crank or the engine is running. It does sound like fuel starvation as it ran and then died. Try jumpering the fuel pump relay-you dont even need the ignition on for that. You should hear the pump running and fuel coursing through the pipes. If you cant, make sure the fuse between the relay and pump is ok. Then check you have power and ground at the pump. If you do, your pump is probably goosed. If I got that far I would whip the pump out, re-connect and give it a slap. Pumps do stick and its only a quick test to see if you can 'make' it run. You would need a new one anyway but at least you found the fault. For ref, you should have 51psi of pressure with the engine off and a jumper in. I am assuming you have pulled out a plug, connected up and have a healthy spark.
Oct '00 E46 330i. Feb '92 525i (departed)