How do I replace the battery shell? You know, the shell of the thing that turns green when powered and red when dying? I have it, but I don't know how to take the little thing out.
I don't think there's a quick way for this, but I can tell you that the piece at the end is supposed to fit in all the way, and stop when you get to the corners of the bottom of it. A better way to explain this: put it in until you no longer see the gold part of it, or until it reaches the orange part of it.
These screws were a bit too tight, but I bet it's for a reason. You should probably put it back on as tightly as it was before.
Hmm, no clue. I've never heard of such a problem. To be honest it sounds like that Gamecube that you have is very worn out, so the best option is to purchase another system. It will most likely cost you around <$40 in total for a good high quality used Gamecube.
I hope you figure out what's wrong, because if you do, you might be able to order parts online and home-repair your console.
You could send it in for repairs, but it would save tons of money if you could figure out what part of the hardware projects images onto the screen, order replacement parts online, and home-repair it. As for the instructions to do said repairs, I can't offer any help except for you to keep looking.
Was it during a thunderstorm?
I'm afraid that the only other option would be to purchase a new system. Unless you were to bring it in for repairs, but I'm positive that Gamecubes are a lot cheaper when bought from the right users/websites.
It's most likely the disc. The only thing you can do is buy another copy of the same game, unless you somehow have an expensive machine that writes microscopic code onto discs (yes, some people are lucky enough to have their own).
You might have to purchase repair parts for it, or if you can't repair a system at home, then buy a pre-owned (preferably replacement) Gamecube console.