So, I found a complete Ms. Pac-Man for Genesis for $3 at Goodwill, but the cartridge did not work, even though it appeared to be in good condition. So I went down to a store that sells Genesis games, bought a used one with a terrible label, and swapped out the boards.
It worked, but I'm curious what could possibly make it not work. I'm thinking it's a blown fuse or capacitor or something. I think it would be a pretty easy solder, but I'm not sure.