Disc not being read

It's entirely possible that your particular copy reads poorly at a certain point of the disc. I'm not familiar with the nuances of the Gamecube disc mechanism, but I know in the past I've gotten certain discs that weren't manufactured properly and wouldn't read right (I bought a certain audio CD that was missing the last 5 seconds on every single track and I exchanged it for another disc that did the same, bad disc runs do happen). So if this is the only game you're having issues with (have you had problems with this disc before?), then I suggest finding another copy of the game to try. Usually if it's a problem with the laser mechanism it shouldn't be too hard to find issues with reading other discs, but it sounds like that's not the case here.