Turns out it's not the screen, it's the console itself.
No matter what power source I use, It keeps happening.
I'll try cleaning it and see if that helps.
If it's the console, then changing the power source isn't going to solve your problem. I would check the cables you are using to connect the console to the screen. Make sure they aren't damaged. It may be that your console is just defective or has some other issues with it. You may want to consider getting a different one. If you aren't too far into your portable, then you should stop with the gamecubes and go for the Wii. There are about a billion reasons why it's better and here are a few that you should consider:
1. Cheaper
2. near 100% compatible with all GC games, plus you can play Wii games too.
3. Longer battery life, and not as hot as a GC.
4. Current, up-to-date help and documentation here on the site.
If you need more, then I can call in our official Wii mascot and advocate
@Shank to enlighten you.