A good link on how to determine the problem with your xbox.
http://www.llamma.com/xbox360/repair/Xbox-360-error-codes.htmHere are a few codes that may not be on list.
error 1002 = drive don't belongs to the mainboard / detection string wrong (check spoof information)
error 1013 = update error, File system roots are lost, wrong or corrupted
error 1031 = E71 Update error
error 1033 = no system files on TSOP or bad/wrong TSOP Flash