"I know that the Nintendo Game Cube uses an ATI chip to render the graphics, but what chip is it?....is it a chip that is used on a PC board as well?"
The GameCube chip you speak of is only
owned by ATI since ATI bought the company that
made that GameCube chip. its not based on any of the ATI designed Radeon chips (although Radeon 9700 was made with the help of the people that made Gamecube's gfx chip) The GameCube chip we're talking about is called Flipper, and its not really related to any current PC technology. the company that made it, ArtX, was a splinter that broke away from SGI in 1997 to form their own company with their main goal of getting the contract to make the GPU for Nintendo's sucessor to N64. (Dolphin/GameCube) these are mostly the same people that made N64's graphics chip, the RCP.
ATI bought ArtX in 2000 for $400M. that is part of the reason why ATI's graphics have improved so much from the Rage128 days and early Radeon days. It was very wise of ATI to buy ArtX rather than let Nvidia get their paws on that talent.
ATI gets to stick its label on the front of every GameCube, even though they did not
design the chip inside it. the next Nintendo console GPU however, if provided by ATI, would truly be an "ATI designed chip"
now that the intergration of ArtX into ATI has long since happened.