actually. i had the same problem.
what you can do is; go into your file explorer and go into e:\dash i think thats where it is, and there should be a file called default.xbe. run that and you should go into a dashboard that has abunch of tools in it. i think its the ndure toolkit, not sure, but w/e. anyway. look around there and i think its under misc or something, but there is an option to install evox. install it and reboot your xbox. after it reboots. there should be a app called remotex in your apps menu. run it and you can back up your eeprom.
it should back up to e:\apps\evox\backup i think.
talk to me if you need any help
if you have aim
AIM:stfu1888
-good luck