BOO-YAH! Thank you guthmund, you are teh 1337.
Mr. Deflok: Yeah, that was my reaction when my friend gave me the 'Cube. "A broken GameCube? Such thing exists?"
And yeah, the GC has an inverted hex/torx screwhead. Luckily my girlfriend's brother has routinely opened his SNES, which I guess uses the same screwhead. lik-sang.com calls it a "GameBit" so I guess that's the official name for it. Also the three-pronged screwhead that they use on game carts and GBA's is the "triwing".
Edit: Ouch, $45 for the laser replacement. Technically I paid $50 for my GameCube from a second-hand CD store (and an additional $15 for the Zelda Collectors Disc

)