If the messages about not logging in mentions both Name and Password being potentially "wrong" it normally does mean the password is the one that it is having issue with.
If it is the Names then the chances are it does not exist and you get a different messages about not finding the name.
This will work for Older (Style) Apple IDs from @mac.com and those issued under MobileMe
It WILL NOT work for iCloud Issued @me.com names
iCloud issued @me.com names only work in iChat 6 and Messages beta as those App also do a Login to me.com that then "Allows" AIM to "See" the Password and allow you access to the AIM network.
Try Opening the Keychain Access app in Applications/Utilities
Find your AIM name and check the Access tab that iChat is allowed to use it.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.4)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.7.4),
"Limit the Logs to the Bits above Binary Images." No, Seriously