you'll need:
-screen: the sony psone screen is a well documented, good choice
-batteries: you'll need either a 11. volt or 14.8 volt li-po or li-ion pack. you'll need a smart charger and charge protection circuit as well. you'll want above 4 amps.
-you'll want a case. several options here. theres vac forming, frankencasing
and premade cases. i recommend the polycase ZN-45.
-gamecube, and controllers, obviously.
-skill and appropriate tools. you will have to know how to solder, and have all the things that go along with that, as well as basic electronics tools (soldering iron, flux, solder, nintendo screwdrivers, wire strippers, wire, sandpaper, paint, bondo/abs cement, meth, wood, and probably some mountain dew)