Ok,
If Port 443 has not worked we have to presume the issue may not be in their routing device.
However it may pay to check to see if it is allowing the iChat Ports to their computer's IP.
iChat Ports
||iChat Ports||TCP||UDP||
|AIM|5190|5190|
|A/V|none|5678, 16393-16402|
|Bonjour|5298|5297, 5298, 5353|
|Jabber|5220,5222, 5223|none|
Note this is the iChat 4 and 5 Range
Add port 5060 UDP for iChat 2 and 3 and extend the group of 10 to 16384-16403 (20 ports)
iChat 4 and 5 also uses an undeclared Random port to do the Screen Sharing part and works if you can and do use UPnP (Or Port Mapping Protocol) to open ports in your routing device.
If they are using Port Forwarding then they may have set these up to an IP that the computer no longer has.
Using UPnP is better if multiple computers. (Port Forwarding only allows one computer to use the ports)
If they have a Base Station then make sure Port Mapping Protocol is On.
Application/Utilities open Airport Utility
Log on with the Manual Configuration Button
Internet Pane
NAT Tab.
IF the KeyChain looks OK and you can Login to a Apple Site with the ID to check it that way try deleting com.apple.ichat.AIM.plist and restart iChat.
(The Home Folder/Library/Preferences)
9:05 PM Friday; April 9, 2010
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"