1 There may be something slightly wrong with the disk which doesn'r show up on all consoles due to minor manufacturing differences between the DVD drives in them. Try a replacement disk from the retailer.
2 The DVD drive may be faulty. Try a handful of other games. If you think it is the drive then contact Xbox support for a repair.
3 Try installing the game to the hard disk (assuming you have one). I have heard from others where disks wouldn't play but they would install to, and play from, the hard disk. After that the disk is just needed in the drive for ownership checking.