First create a new ERUNT backup. This must be done first.
Download LNK assoc fix here. Unzip the file, then double-click the REG file to import it. Reboot.
After that let's try rebuilding the icon cache.
Open Task Manager, choose all instances of "explorer.exe" (take care to choose just this filename). Your desktop will disappear. Don't close Task Manager just yet.
In Task Manager, click File - New Task, type "cmd" then click OK. In the Command Prompt window type in:
del /f /a /q %userprofile%\AppData\Local\IconCache.dbClick New Task again, type in "explorer.exe" then click OK. Your desktop should now come back.