I think Slavy is pretty close here. That B/W wire is sort of a switched ground in the system with all the interlocks. Try to jump the solenoid terminals (the 10 MM nuts) and check to see if you have 12 Volts on the 2 smaller Y/B and B/W wires when you hear that click.
However, I'd almost bet a case of beer that you don't have a bad starter solenoid. Too much coincidence after just draining the battery in the park position. I think something else happened during the initial "what the hell is wrong" testing
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Also, you mentioned that you jumped it, it idled, and then died when you tried to drive it. Did it idle normally or did it idle rough?
Do you also have a nuetral light on the speedo when you try to start it?
Do all the lights and horn work?