Hi Scott,
iChat uses port 5190 to login using the TCP protocol and gets certain Buddy List info back on port 5190 on the UDP protocol.
For some modems and routers this seems to be a problem.
Try opening iChat and logging out of AIM from the IChat menu.
Then go to Preferences > Accounts.
In there select the account/screen name you are using.
Select the Server Settings tab on the right.
Set the port to 443
Log back in to AIM
This makes the Login happen on port 443 instead of 5190 and separates it from the UDP data.
Another problem might be that your Login preferences held in com.apple.iChat.AIM.plist are corrupt.
Go to Users/(your account)/Library/Preferences and delete it.
Restart iChat.
This .plist will be recreated from the iChat defaults and your Keychain info.
On some occasions you will see the Start Up Screens again but the info should be pre-filled form your Address Book.
10:46 AM Thursday; July 26, 2007