I reflowed the coil connector, PTC pins, and relay pins. No dice.
The PTC is in a black box, so I can't tell if it's damaged or not. I suppose I could desolder it and see if there's anything shaking around inside....at no point did it ever feel warm to the touch, either.
When I press the degauss button, I do NOT hear a relay clicking, so is it likely the relay is bad? I already ordered a replacement PTC and finally found the correct relay after a bit of searching...maybe I should just shotgun in replacement parts for the entire circuit...