Got two Gamecubes from ebay a few weeks ago for 10 including postage for the pair. No power supplies or controllers. Borrowed a power supply and both power on with video display (using snes composite cable). One reads discs, the other (purple one) doesn’t.
Plan is to strip them both down starting with the purple one, good clean etc. Change the power socket for a standard socket and possibly video out through rca sockets rather than the nintendo connector Power socket the main priority – nintendo composite cables are cheap to get.