I have a friend with a 2001 neon. The car would stall at least half a dozen times a day. We finally figured out that there is a wire cluster that runs under the battery. Well the acid from the battery ran down and strted to corrode the plastic and the metal was grounding out with the battery tray. all you have to do is clean up that section and recover the exposed wires.. I hope this helps someone..

I would think that is it for real check all those wires and make sure the grounds are hooked up. Mine was stalling like that and i did something around my starter and fixed it I forget sorry but check those wires under the batter like you said.