Hi,
You don't need to to delete the whole app.
Provided that you have not been logged in by some means and deleted your Buddies they will be still there in your Buddy List that is held at the server. (the App links with the Address Book and links in Real Names on the computer)
If you have the Password and it worked before for iChat then you should try logging in at the AIM settings page
(If it is an Name that logs in to AIM)
IF it is an @mac.com or @me.com name from MobileMe but never been used with iChat then it could be that it is too long.
The AIM servers use passwords that do not exceed 16 characters but you can have longer ones at Apple.
I really need to know what sort of name you are trying to Login with as there are many variables.
8:22 PM Tuesday; April 24, 2012
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
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