I have just correct this problem on my sisters new Imac. She had an AIM account for Ichat. We could see each other in the Buddy List, but Video Chats, and Screen sharing could not be totally initiated. I could attempt to initiate a Screen sharing with her, from my side it showed the request for permission was sent to her Imac. From her side, she saw no permission window at all. When she tried to come to me, from her side, the permission window would appear, but after I granted permission, her side acted like it never received this grant and in essence the session initation hung and timed out.
The fix was to bring up Ichat on my sisters Imac, and delete the AIM definition under ACCOUNTS in the PREFERENCES. Then create a new AIM definition (+ at bottom of screen), this time do not put the @AIM.COM as part of the USERNAME. Apparently, adding the AIM.COM to the user name stops Ichat from initiating the sessions. Once we did this, Ichat worked without any problems.