Is your gamecube controller working for other games? Are you trying different controller ports, in case one of them is broken?
Perhaps you need to find an options menu where you can turn on the use of a Gamecube controller. Or maybe once you use a Wiimote for anything after you click "start" to run the game from the disc channel, it won't realize the Gamecube controller is plugged in. Trying skipping any cinematic intros or getting through the start/load menu/whatever using the Gamecube controller. This is how you use a Gamecube Controller in Super Smash Bros. Brawl, so maybe it's similar in all-stars.