Be careful with the jump starting, you can fry a body module nothing flat. If your battery started the car one night, and was dead the following morning I'd be suspecting some kind of parasitic draw. Like an interior light staying on in the trunk, glovebox, door not all the way closed, something like that. If your car is losing power and then getting power (as in a bad/weak battery connection or cable) the security system could be freaking out. Like I said though intermittents are a real beyoch. Can you think of ANYTHING at all no matter how small that was different from starting and not starting?