Common Dreamcast problem...
Some discs simply can't be read by certain systems. Those GD-ROMs were so incredibly sensitive...
Try popping in one of the other AitD discs first (it is multiple discs, right?). When I first bought Skies of Arcadia, the first disc was unreadable. I simply popped in disc 2 and it booted. After choosing to start a new game, it asked for disc 1 and I was all set from there. After that, disc 1 has never failed to boot.