Car wont start unless door is open

Mattax said

Yes.
The middle one goes to the neutral safety switch. It allows the starter relay trigger to ground when the transmission is in P or N.
The side wires connect to the reverse light switch. One is hot whenever the key is in run, but not start.

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Explain further, the neutral/ reverse switch has 3 terminals and two switches. The center pin is switched to ground in park/ neutral and goes to the starter relay for neutral safety, allowing the siwtch to activate only in those two shifter positions. The outer two are reverse lights, so the 2nd and 3rd wires in that harness are power to the reverse switch, and the 3rd wire feeds off TO the reverse lights. It routs up through the bulkhead, down to the left side kick panel connector, and on to the rear harness and reverse lamps

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.