When you deleted the game, did you also delete the .ini files, Skyrim.ini and SkyrimPrefs.ini, located in the My Documents\My Games\Skyrim folder? These are typically not deleted when uninstalling the game, so if you haven't, delete them yourself so the game creates new default .ini files.
The next step would be to verify local content through Steam.
Possibly when you deleted the game it might not have removed all the files in the Data folder.
Check the Data folder within the Skyrim folder It might look like something like this
C:\Games\Steam\steamapps\common\Skyrim\Data
Problem resolved.
Thank you very much for finding the time to help me. Without you I would still be sitting here with my thumb up my ***.
Much appreciated. )