I tried logging out and wanted to log back in as you described clicking the appropriate link at the top-right - what I got was the main page, and at the top it read that I was logged in... without me entering anything.

 I then logged out again and emptied the cache. When I then clicked the login link top-right I was presented with the login page requiring me to enter user/password. So I think you'll be fine once you empty the cache. Perhaps try first to clean out just the cookies and see how that works.

 Kalli