Well...
Do the uninstall procedure like this:
First do a standard uninstall. (Control Panel\All Control Panel Items\Programs and Features-> Uninstall The Elder Scrolls V: Skyrim)
Next, delete your skyrim folder under C:\Program Files (x86)\Steam\SteamApps\common\
Then delete your Skyrim directory under Documents\My Games (Back-up your save files, but don't use them, ans start a new game)
Then under C:\Users\[Your Username]\AppData\Local\ - Delete the Skyrim folder that is in it.
(You should enable to see the hidden files under windows to delete that folder.) HOW: (View - Options - Folder Options - View - Advanced Settings: Show hidden files, folders and drives)
Go to your Steam folder. Delete the folder named appcache. (Important)
Use Ccleaner after all this (http://www.filehippo.com/download_ccleaner), Go to the Registry tab and hit -
In the Options tab go to Monitoring and uncheck: Enable System Monitoring and Enable active Monitoring
Reboot your computer (Important)
Then install your game again, from scratch. !!!!
*** You don't need to uninstall Steam. ***
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Also, revert your GPU settings to the default settings.
If you could play at first place without problems, then something interferes with your game.
Also, have you installed recently any utility related to your GPU or game ???