ive heard of this problem before. the auto shutdown relay is clicking and not starting. if i go and start the car it will start but will turn off if i dont keep my foot on the gas. after that the relay thats clicking
Did you check the actual battery terminals? They will crack and stay loose even when you tighten them all the way, and cause problems like this. Check also for corroded cables. Which engine is it? 2.7, 3.2, or 3.5?
That sounds like a security problem, (SENTRY) now that you mention it starting and stalling. There is a separate system that operates the starter solenoid and the BCM can shut it off if it thinks the car is being stolen, among other things. It will let you try to start it once, then it will kill the cranking system.
This job is best left to the dealer, it could be as simple as a bad key circuit, or the BCM itself. I would at least let them look at it, they could verify whether or not this is the case.