I'm getting the exact same thing.
Went to the Adobe website, and I log-in there just fine. But the Creative Cloud app on the desktop? Can't log-in to that. I get the "You're signed out." message as well.
Is this something going on at Adobe?
John T Smith's linked solution worked for me.
Correct Answerby Romsinha on Apr 19, 2014 11:51 AM
Please navigate to C/Users/User Name/AppData/Local/Adobe/OOBE/opm.db and delete it(Windows).
Mac: ~/Library/Application Support/Adobe/OOBE/opm.db and trash it.
Enable user library: http://helpx.adobe.com/x-productkb/global/access-hidden-user-library-files.html.
Launch CC desktop and try to sign in.
The only thing I'd add is to remember to go to the Activity Monitor to quit Creative Cloud.