pretty sure SKIM theft system can cause a start and die. Usually, they start and die 5-6 times, then nothing at all ( i think). The only way to know for sure would be to use a scan tool to see if the theft system is indeed activated.

I dont think, 04 computers did not have SKIM just because it was an 04. Or use an anoid light to check and see if the injectors quit pulsing when the car quits running.