Hi,
If you had navigated to the /Home Folder/Library/Preferences you will have seen that it contains the ByHost folder and that some .plists do "appear" to be repeated in there.
So...
Erasing the whole disk/Drive would had deleted those .plists 😉
You say you now appear to Own them and they don't seem to be duplicating themselves like they were before.
However both your regular account and the Test Mac User Account still can't Video in iChat using your Google ID.
You have said that the Buddy is using a Mac and iChat with their own Google ID
You had previously checked that the Video Chat And Audio Chat items (Video Menu) were ticked/enabled as were the Show Status items in the View Menu.
You had previously posted a Picture that show s the Connection Doctor has no problems with the Internet Speed (and what iChat is supposedly can do).
AS we can assume now that it is not the .plists we have to consider the Firewall on the Mac
System Preferences > Security > Firewall.
If Off then the issue moves to the router.
If On open the Advancedd Button
In this pane the "Allow Signed Software" item needs to be ticked/Enabled and iChat and IMAgent need to be in the list
Stealth should NOT be ON.
This block Pings coming to the computer (usually on the LAN Side) being reponded to. If you tried pinging the IP the computer has from another computer at your Home (or office) the Mac would not respond.
However iChat Sends a Ping during the Connection Process to confirm that the IP that is responding to your Visible Invite is where you sent the visible Invite to.
If Stealth is Off then we need to check the Routing device you have.
Router
You should be able to access this with a Web Browser.
Using UPnP will open the ports iChat needs (the app tells the router when it needs them and they close after a period of non use)
The router may have other 'features' such as Ping Blocking that need turning Off.
Some Firewalls on routers can be an issue.
It may pay to tell us what make and model you have and what has been done to set it up for iChat.
(devices are so varied that it can take a long time to describe them all).
8:00 PM Saturday; January 21, 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