This is a issue that ghosts since atleast last year that LL don't look into. I havent been able to log in to my avatar for over 24h now and tried hundreds of locations, so if you cant log in after try say 5, this is not at all the issue you have.
Stated above to check your internet connection would seem highly unlikely if you're able to post on forums, and to save the pointless firewall discussion this is not the problem either.
Most likely there is nothing you can for sure do at the point you're entirely locked out but hope LL gets the ass out of the wagon and starts to investiogate, but since it was reported in september 2013, nothing has changed.
I have also tried the invalid characters in group title etc, to no avail.