Update:
I tried to diagnose the generator with some manuals and diagrams that I had found online, and after putting an honest effort into it I was able to get nowhere. In response your advise; both breakers weren't tripped and I made sure the power cord was plugged into the socket in the power cord bay. I don't have a transfer switch on my generator. I ended up bringing the RV to someone to have the generator looked at.
As far as the refrigerator goes, fantastic news. After letting the refrigerator run on electric overnight, it seems to be working flawlessly. Both the refrigerator and freezer are at the proper temperatures; I guess it just takes a long time to reach proper temps.
Thank you both for the advise though; I lucked out with the refrigerator, but the generator is going to be much more efficient for me if I just pay to have it fixed. At the state my generator is in, it's out of my expertise - and I'd hate to damage the generator more than it already is.
