Again, thanks to all for the information and advice. BTW, before this problem happened the AC cover had never been removed (in case anyone is wondering if a prior repair or something caused this).
I'm heading over to the RV now to clean up the terminals and better assess what it looks like. I'll take pictures.
I've printed the instructions for testing for continuity and will look at the wikihow links Don sent before testing. I only have the very cheapest multimeter (the one you get for free at Harbor Freight). I'll go get a better one before I test.
So, to summarize:
1. test for continuity
2. if that's good, purchase the correct klixon and run capacitor
3. wire them in, insulate as needed and and secure them somehow (zip ties?)
Did I get the above steps correct?
Also, is there any chance the capacitor is holding any charge? the RV hasn't been connected to AC power in 4 months.
Don, I'll PM you my contact info, we can definitely have some BBQ when you're in Dunedin!