Judging by what you have in that screenshot there, the file system did become corrupt at one point. It looks like that truely is a 0kb file for some reason now probably due to corruption. You have a few things you could try;
If there was important data contained on that desktop then you might consider using one of the free file recovery tools available to see if you can recover it before you go further..
Login as another user, delete the file, recreate a folder called Desktop
Log back in as the original user with the issue and they should at least see the default icons from the All Users profile on the desktop now, and it should function normally.
Keep us posted