Car wont start unless door is open

In the diagrams the alternator output wire is labled R6.
Follow it to the battery. Notice there are no switches between it and the battery positive.
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Even with the key off, those wires are always hot unless you disconnect the battery!

The alternator is the main power source when the car is running.
To keep the car running, about 5 amps flows from the alternator to the ignition and alternator's rotor (aka field).
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When the battery is low on charge, it will draw current too. Immediately after starting, this might be as much as 20 amps.
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Now there are 25 amps flowing out of the alternator.
Turning on the headlights, wipers, stepping on the brakes, etc, all will increase the load on the alternator.
Parking lights ae about 5 amps, Headlights around 9 amps, and heater on high close to 10 amps.

Now on your car, there is an extra connection in the alternator output as well as the run wire.
It doesn't take a lot of resistance to generate heat in a connection that is seeing 20 or 25 amps for long periods of time, such as driving at night in the rain.