1987 Trans Am - 5.0L TPI Auto - Weird starter problem

My friend's son installed new rear speakers in his 87 TA. Afterwards, it wouldn't start. This car is equipped with an aftermarket alarm that is disconnected. I tried jumping the starter solenoid terminal
to the hot (from battery) and it would just arc. I jumped hot from the battery lead to the post that actually goes into the starter and the starter cranked until I disconnected the battery. I think the purple (solenoid) wire is shorted to ground but I am having trouble tracing it because it is grounded and I get continuity between it and many other things. Has anyone seen anything like this? I had the started bench tested and it is fine. I found a plug near the fusebox with a thick yellow and thick purple wire. The purple plastic end of the plug is a little melted but I can't find where this plugs in. Any help would be appreciated. I haven't tried jumping past the ignition switch or neutral switch because I don't want to short anything out.

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