Download the attached file and save it to your desktop. Right click on it and choose "Extract All"...extract it to the desktop, too. Copy the extracted file (fixdesktop.reg) to a flash drive, floppy, or cd. Navigate to it on the broken machine, right click on it, and choose "Merge"...accept the change.
Reboot. Do you have the desktop after the reboot?
fixdesktop.zip 579bytes 96 downloads