Same problem as the rest here....gui interface is gone. There is a GameoverlayUI.exe that runs while skyrim is running. Am I to assume this is part of the issue?
Don't tell me they used flash to build the gui interface for this game??
GameoverlayUI.exe is the Steam in-game overlay. That .exe process runs alongside every game you run through Steam that supports the overlay, not just Skyrim. So no, that .exe is most likely not your issue.
You can disable the Steam in-game overlay and see if that changes anything, just as a test, but I doubt it will fix your problem. In Steam, go to the Steam dropdown menu -> Settings -> In-Game tab -> untick the "Enable Steam Community In-Game" box.