I had the same problem with my 02 GT. It might be your Mass Air Sensor. When i put in my CAI i cleaned my MAS and the problem stopped (knock on wood!). Try cleaning off you MAS. if that doesn't work try starting the car with the sensor disconnected. if it starts up than its your sensor. if not ?????
One thing though is that if you do this you'll have to disconnect your battery for like a half hour afterwards or else the check engine light will come on. After its been disconnected for a half hour reconnect it and then drive the car around without using any electronics (radio, A/C, Heat) to put a good charge back in the battery. (i don't know if this is neccesary but i did it anyways, not exactly what you would call a "motor head")