Pokémon Silver lives! Now I wish I hadn't gotten rid of the other two...for multiple reasons!
It was arduous: trying to unscrew the cartridge, removing the soldered dead battery without scratching the circuits, securing the new one in with scotch tape...but Pokémon Silver is saveable once more!
So I figured since I have the one game, I'd use Stadium to get all three starters, right? Well, apparently, it doesn't let you withdraw from the N64 box unless you have the National Pokédex. Which means unless someone I know is lucky enough to have a working version, I'm stuck without my main party.
I'll enjoy it while I can; I did fix it, after all! But I won't go past the Day Care until I know for sure what I'm doing.