Same thing happened to me. So I closed the launcher and opened it up again. I can start the game just can't login. Possibly issue with servers right now.
Since I'm getting the problem again I feel the need to update this, all of the stuff you guys are suggesting I've already tried, there seems to be no fix for this in any possible way, so basically Ze…
Since you got a workaround that helped at least someone, i hereby grant you an "awesome" <img class="emoji" src="https://forums.elderscrollsonline.com/resources/emoji/smile.png" title=":smile:" alt=":smile:" height="20" />