Here's the final result:

The thermal limiter and the plug that goes into it were both corroded and cooked, so I replaced them.

I found one ground that was able to be tightened, but I'd hardly call it loose.

The fan motor was making funny noises - when it finally came on after replacing the limiter and plug - so I replaced it. The first new motor ran for about 20 minutes then died. So far the free replacement is doing well. And now that I've replaced the thermal limiter I have four fan speeds again, rather than the one I've had for the last three years.

Thanks, SubFord, for your very quick responses, and thanks to the FTE creators and maintainers - you helped this rookie get the job done.

TheRed