Sounds like the disk or your console is having problems loading the data off the disk. This would mean that either your disk is faulty, or there's a problem in a certain part of your console. Either one would mean either a replacement Fifa 08 or even a replacement PS2 if the problem still persists.
You say you've tried 20 disks (is that 20 Fifa 08's or 20 other games?), and there is still a problem aswell as with your friends console? I think both of your PS2's must have some kind of internal problem, i would find it hard to believe that 20 disks all give you the same problem....?