HI,
It used to be that for iChat we used to have to tell people to set up their Google Account using their Google ID exactly as it shows on the Google Web Mail Page (Or iGoogle) to make sure they had to "right" ending.
The Server is talk.google.com
This does not follow the format used by other Jabber servers which take the last part of the ID and pulls that through to the Server Setting tab and this is why iChat and the versions of Messages have a separate Google option to add the Account.
The next issue would be to then check the Mac firewall
It is in System Preferences > Security and Privacy > Firewall.
It will need Unlocking.
What used to be in the Advanced Button is not in the Options Button
In here if the Firewall On then the Allow Signed Software needs to be Enabled and Messages and IMAgent need to be in the list.
If you have to Add Messages or Enabled the Signed Software bit it will pay to restart the Computer.
The System should add IMAgent itself (Or at least ask you to confirm)
Next we have to consider the Router.
If you used Port Forwarding with your Previous OS (or even computer) you may find the IP the computer has at the moment does not work for the Port Forwarding you set up.
Ideally use UPnP if you device has it.
It allows for Multiple computer s to use the same ports. The ports open when the app needs them and close after certain period on Non use.
For Messages and iChat it also allows Screen Sharing to work as this part uses a random port.

9:07 PM Wednesday; July 25, 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