The fact that it will turn over in no way eliminates the possibility of the ignition switch. When those go bad, or start going bad, the symptoms are random and weird. It may also be your Body Control Module, or any other circuit in the electrical system, as this guy found:
http://www.grandprixforums.net/weird...g-bcm-865.html
I would start with the simplest possibilities first. As Bill suggested, make sure it's not a charging issue (battery, alternator, wiring in between/grounding, etc), as those also cause bizzare issues as the power supply reaches a low point. If you find something is pulling a strong draw with the ignition off, best way to narrow it down/get a starting point as to where to look is to start pulling fuses as Bill suggested.
