Looks like this happened before Unable to log in to chat.
I use firefox 11.0. Followed the test on all looks ok, but I can't log in.
It seems to be some issue with your sessions, I have cleared your sessions info from the moderators panel in your account (forced logout), that should do the trick.
Log back, it should be working.
I get a similar effect when logging in via Gmail, logging out from Gmail in to another account while using Ask Ubuntu and opening chat. While it says that i am logged in the main site, the chat will say I am not logged at all and will refuse to even login.