Progress Report:
I accidentally did the heat-up-the-capacitors trick by leaving it locked up in an outbuilding at 100 degrees for a few hours today. Obviously this is not the best way to go about it, but it worked, so to speak.

It was hot enough that it worked flawlessly and immediately when I pressed the power button, so that would indicate failing capacitors, correct?

Anyway, it sounds like the diagnosis is confirmed pretty much, at least I think so.

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