Easy, each drive looks different. You can find a picture of the Thompson Drive on line. If you have the Thompson Drive you are screwed. If you are no longer under warranty and the problem is getting worse than you may need to change out the drive itself. Not as hard as it sounds. Google "Thompson Drive for X Box" this is what I did. I found a picture that showed the 3 kinds of drives. I got lucky but my roommate had the Thompson. You'll see that Dirty Disk screen more and more. Best thing is, when he sent it to Microsoft to get fixed, he got another busted ass Thompson Drive back.
Either way, you'll work it out. PM me if you can't figure it out. I'll look for the pic if you can't find it and send you the link.