I have seen some computers with problem seeing the desktop icons before.
Once login, the computer reboots.
If this is the same situation you have, I would suggest we format the HDD before the reinstallation.
Please back up the data first if needed.
If still the same problem after format and reinstalling of the OS, I would suggest boot the OS in safe mode.
If safe mode works, then we need to check the hardwares on the computers including the video card, RAM...etc.
Hope this helps.
Tech Manager, WPTinc.