The Gamecube controllers dont use any popular computer interface, its designed much like its predecessor, the N64 controller. It uses only 1 wire to transfer data, so you would have to build a complete circuit to drive it and interpret the data so that the computer can read it. To build one, youd have to have at least above average knowledge in electronics.
http://www.st-hans.de/N64.htm. Thats the guide to the schematic and parts list. Its in Spanish, but you should get by ok. AFTER completing the circuit, youd have to hope it works with the Gamecube controller, which might have been updated. Even if a single pot is miscalculated with the new controller, it could screw up the whole circuit and make it dysfunctional.

Still wanna do it?
As for the Gameboy screen, why the hell would you want to in the first place?
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Still poor, leave me alone.
Should really make an avatar. Nah. Nevermind.