Do-It-Yourself Story

I unplugged the device, opened the case, shorted the capacitor's terminals together with a screwdriver (safety precaution--always do this with a microwave oven--the stored power in the capacitor can pack a wallop if you don't discharge it first), and just looked around. I quickly saw that the wiring to one terminal of the thermostat was black and melted. Nothing else looked amiss, so I figured this was the problem. (I also figured out how to read the wiring diagram and confirm the problem with my ohm meter, but even if I couldn't have done that, I was already convinced that the burned thermostat was almost certainly the problem.) Ordered a new thermostat and installed it when it came. I had to cut off the burned connector and crimp on a new one I got at the local hardware store. Wrapped the new terminal+connector in electrical tape for insulation. Put the cover back on, tested the microwave, and all was well. Took about 30 minutes total.