The Message from AIM about Logging in too many times can be waited out (there is little else that can be done)
If it is happening continually then you need to look at you Network and whether it is maintaining enough of a "Always On" presence.
Wifi Network can suffer micro breaks that cause Buffering in downloads but not complete loss of connection plus delay in going to new pages in a Browser or delays in fetching new mail.
However iChat and Messages in Mountain Lion require an "Always On" connection.
Your Process so far seems to be correct.
Insert Appropriate DVD
Select Optional Installs
Launch the Optional Installs Package.
Your Specs say OS X 10.6.8 which is Snow Leopard.
This is the correct method and seems to tie up with what you are seeing.
Lion and Mountain Lion need you to do the Restore Process. (it is like Archive and Install was but uses Apple's On Line store to get the Software).
I can see that Lion (if this method was an option) might have issues if the Messages Beta had been installed but you are using Snow Leopard.
I cannot think why it might not allow iChat.
I would do PRAM reset as a first option.
Shut down the computer.
Restart it holding down Apple/CMD ( or ⌘)+ALT( ⌥)+P+R Keys until you have heard three Start Up Bongs.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
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