Ok,
In that case we are talking about your end.
First of All go to the Video Menu and double Check the Microphone Enabled item is ticked.
If Speech is moving the System Preferences > Sound > Input bar but not the iChat one then this may be the cause.
Then try a Video Chat and click the Mute On and Off (Leave a few seconds in between to get that data written to the .plist) Technically when you end a chat the Mute should be ON again at the Next chat (it will not get set to Off between chats)
If those to things do not help...
With that info you probably need to delete
com.apple.ichat.plist as this .plist hold the volume settings for iChat. (This is despite not being able to adjust it in iChat's own settings)
This .plist is found in your Home Folder/Library/Preferences and should be Dragged to the Trash.
iChat then needs to be restarted.
Restarting iChat will make the .plist get re-written from defaults held in the app itself.
IMPORTNT NOTE
Deleting this particular .plist deletes all the settings you may have changed in iChat's Preferences with the exception of the Accounts pane (this is read back from the Keychain)
That will be:-
Font
Any Colour you chose for the Font.
The Colour of the IM itself (Balloon colour normally)
Whether you Save Transcripts, and any Sub options in iChat 4 and 5
Anything in the general section.
Anything in the Alerts section.
These will need to be re-set.
8:16 PM Tuesday; April 12, 2011
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"