Oldsmobile Cutlass Supreme Sl Randomly Dies

My cutlass will randomly die on me, it starts up just fine when I leave my house to go to the store or something but then when I try to start it up to return home it will sometimes start up but only for a few seconds before it just quits. It has been doing this since I had the fuel pump changed. It also needs a new transmission as that part has just begun going out. I have had the idle air control and throttle position sensors replaced but that didn't solve the problem. Could it be the fuel pump is faulty or is there another sensor that might be going out or could it be connected to the transmission failing? The check engine light doesn't come on, in fact, no no lights come on to indicate what the problem might be. Can anyone help me figure this out?