well as for me i had the same problem..."dirty disc error" was a pain in the ass for me...but once i uprageded the hdd and my dvd drive..i have not seen that dreaded message again.
if u have been using the same media for ur xbox backups them im guessing ur dvd drive has lived out its uselfullness already. i didnt start seeing that message till about a year and a half of using my backups. sorry but im pretty sure ur options are either buy an new hdd or dvd drive.