This is pretty hard to diagnose via a bbs, but it sounds to me like a fuel starvation problem. Since it's starting, It sounds like your pump is going on when you turn the ign. on, then shuts off, as it should, but not restarting after you beging cranking/ startup. The ecu sences when the engine cranks and starts, so re-energizes the fuel pump relay, but it sounds like this isn't happening. You can check for this by either putting a test light on the hot lead from the pump relay, or at the pump. Another way is to check the rail pressure when you turn the key on, and see if it stays up when you start the engine. I'm guessing you're going to find it quickly drops to zero.
One thing I will say, is that this isn't likely to be related to the TPS at all.
Try cleaning the wire in the Air sensor which the air passes through right after your air filter box. Take a q tip and some alcohol and clean the wire that runs inbetween the cylinder.
The other thing i am thinking is there may be an Idle control valve that is sticky. I think i remember Eric the Okie saying that is located behind the intake manifold, But I have never done that myself, but from your description it sound like a possible cause..