Hi,
Nearly three months later after a solved issue is likely to be a completely different issue.
However I do note you have only just updated to Mountain Lion and Messages.
I would check the name you have for Google in System Preferences > Mail, Contacts and Calendars.
The email ID s you have tend to get listed hare and some are also Active for Messages.
The Mail App up until Lion kept the Mail Account info separate from the iChat (Now Messages) logins.
The Google mail server allows you to access the server as Username@googlemail.com and Username@gmail.com
The Google talk server is much more fussy (Secure) than that and will only accept the way the account name is spelt on the Google Mail Web Page.
I am suggesting that in Mail you had one name set up and in iChat another but now the Mail one is active for Messages and is not Logging in.
9:09 PM Thursday; October 18, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously