Hi ellejelly87,
This can be about the way your router is set up.
iChat uses one port to login to whichever server you are logging in to.
It uses another for the Visible Invite.
It then moves to another for the connection process.
The Connection Process involves another invite and both ends also PING each other to confirm that where the Visible Invite came from and went to are the same places that are responding in the Connection Process (it's a feature to stop what are called "Man in the Middle" Attacks).
Testing between my iMac and MacBook Pro I can say the iMac's green light does come on before the Invite arrives. The Preview (video Pic) at the receiving end is there but currently hidden in the Invite until you click on it to then Accept or Not.
Can you test ?
When someone sends you an Invite and the light is On, does the Window Menu list the Invite.
This may tell us whether the Invite just happens to be Off screen for any reason (Normally on a Second Monitor that may not be present).
In iChat Menu > Preferences > Alerts, when you have the first item drop down set to Video Invitation do you have the Auto- Accept AppleScript active ?
If this is iChat 5 or earlier do you have the Chax Add-on that can also be set to Auto-Accept (by Buddy)
9:24 PM Thursday; January 26, 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