Ok,
Two things (possibly three)
1) Open up Activity Monitor (Applications/Utilities)
In here with the All Processes choice in the top drop down should show iChatAgent running when iChat is.
They will not be together but are likely to be close together nearer the top (most recently launched item)
Is yours showing iChatAgent ?
2) Whilst In Applications/Utilities also Open Console
Use the Log Icon to left to display the list.
Are there any comments in the Console or System Log about iChat and possibly Not finding iChatAgent ?
3) Navigate manually to Hard Drive/System/Library/Frameworks/InstantMessge.framework (See bar at bottom of Pic)
Does iChat Agent appear in here ?
4) Open Terminal (Applications/Utilities)
Copy and paste the bold text below when you have Quit iChat
/Applications/iChat.app/Contents/MacOS/iChat -errorLogLevel 7
Hit enter.
This will cause Terminal to Launch iChat and create a log whilst doing so.
When iChat has logged on make a not of the line the log is up to. (Grab a Copy and Paste it to TextEdit).
Now start a IM Text chat.
As iChat is unlikely to do this Bit Force Quit if Required.
Grab the next part of the Log (Copy and Paste to another TextEdit).
Now Quit Terminal.
Post the two logs here.
A Repair Permissions (First Aid tab in Disk Utility (Applications/Utilities) and the Repair Permissions button) - may cure this if iChatAgent is there - so I would try that.
I suspect the Terminal Log will highlight a problem that will need a reinstall of the iChatAgent.
Of course it maybe the Link commend from iChat itself that is the problem.
We will come to that though after looking at the Log.
8:04 PM Wednesday; April 8, 2009