HI,
When you have logged in to the Google Mail web page does your name there show as username@googlemail.com or username@gmail.com (I can see in ichat you have used @gmail.com)
Whilst it seems that the Mail app can use either and get your Mail iChat needs it to match exactly as it does when you log in to Google itself in a Web Browser.
9:21 PM Wednesday; February 15, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.3)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously