A few days or a week ago now Steam said it had an update for itself and ever since then I can't play Skyrim. I click Play in Steam and it brings up the Launcher. I click Play in that and it asks me if Skyrim can make changes to my computer with a User Access Control dialog. If I say Yes, it goes away and then comes back to the launcher. If I say No, it asks me a couple more times before eventually just coming back to the launcher again.

I tried removing all of the mods I installed with the steam workshop and un and reinstalling - same problem. Then I found that the Nexus Mod Manager's mods survived the reinstall, and disabled all of those before un and reinstalling again. Still the same problem.

What can I do??

Move Steam out of Program Files.
https://support.steampowered.com/kb_article.php?ref=7418-YUBN-8129

I can't believe that worked. I already had it installed in a different folder, but I tried moving it to a new different folder and it did work! Thanks!!