iCloud on macbook doesn't recognize correct Apple ID/password
I've been trying to sign into iCloud using my CORRECT Apple ID / password combination but it keeps telling me my password is incorrect.
I know this is not true because I just used the same Apple ID / password combo to sign into this Apple support community (which was required in order to post this message). Also, I have had no problems using it to download apps on my iphone from the App Store.
I've tried changing my password (as prompted to do by Apple Support, since there is no password recovery) and while my iphone / App store sign in recognizes the new combination, my macbook doesn't.
Please help.
Thank you.
MacBook Air, iOS 6.0.1