When logged in as a domain user, have a look in the registry. I’m guessing that some AD group policy is changing the location of the desktop of other required system folder and that path doesn’t exist for the Windows7 machine. Or possibly that there is some access problem for the paths they specify. Compare them to a local user.
HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders
and
HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\User Shell Folders
The User Shell Folders are expanded (environment variable expansion) into the Shell Folders. So really you only need fix user shell folders then log out and back in.