HI,
Your specs say OS X 10.6.8 which would be iChat 5.x.x in Snow Leopard.
This version by default tries to login in to the AIM server called login.oscar.aol.com on port 5190 using the TCP protocol.
An internet connection is made up of 65535 of these so called ports (more like TV stations)
Most routers have ports up to port 1024 which means some of the iChat Login Ports are above this.
Two ways to Solve this.
1) Change the Login port iChat uses
2) Change the way the router opens ports.
For 1) go to iChat Menu > Preferences > Accounts
Highlight/select the AIM account.
In the Info Tab deselect the "Enable this Account" to make sure you are Logged out.
In the Server Settings change the Port to 443
You can decide not to use SSL as well if you wish (the server name automatically loses the leading "s")
For 2) log in to the routers set up pages and make sure it is doing UPnP
This allows the computers to tell the router which ports to open. It also allows multiple devices to use the same ports.
For iChat this allows it to Screen Share as this happens on an unlisted random port.
Opps forgot a couple of things.
If you are using an APple ID registed at Apple ending in @mac.com @me.com or @iCloud.com then the passowrd at Apple has to be 16 characters or less to work with the AIM servers.
Additionally the iCloud issued @me.com and @iCloud.com one require you to use iChat 6 in Lion or Messages in Mountian Lion due to changes Apple made to the security of letting AIM "read" the passwords.
9:38 PM Sunday; June 9, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.4)
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
Message was edited by: Ralph Johns (UK)