Car wont start unless door is open

I'm still not seeing anything that relates specifically to your problem. Actually there "should" be nothing damage wise in the engine bay that could cause the start problem, as there is no courtesy lamp wiring in the bay. The comments I made earlier were more "general" and also if someone had hacked some anti theft device in.
Good point.
Maybe something to do with how the buzzer ties in with the key switch.
However, when the buzzer is grounded, the car starts every single time. And when the buzzer is not touching anything, it doesnt start.