Not enough info really.
The Mac could be an older one sold as new and have Snow Leopard and iChat 5 running on it.
This would mean any iCloud issued @me.com name from Apple would not work.
This is due to a change brought in for iChat 6 (Lion) and Messages in Mountain Lion where the app logs in to me.com which then allows the AIM servers to "See" the Password.
Also only @mac.com and @me.com names work as AIM valid Screen Names.
The new @icloud.com ending ones also works as AIM Screen Names (in iChat 6 and Messages only)
iChat version ?
Screen Names issued Where ?
What OS version ?
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