So recently I had this problem with iChat where every time I'd try to screenshare with somebody, I'd get an error from iChat that said it could not connect because I was already engaged in another chat.
Actually, the exact error message is:
"iChat can’t start the audio chat."
"Your computer is busy in another chat."
After a quick Google search, I found that lots of users recently seem to be having this problem, as the Apple support discussion board has several related posts all dating within the past two or three months.
I ran across this one post in particular, and while I didn't use the same solution that the poster found from Ralph Johns, I did find this one simple solution from a poster named Lanny who gave the following instructions:
In the future, if it happens again, turning off Facetime, in the FaceTime Menu (also Command K), not quitting FaceTime, and reopening iChat will fix the issue. You won't have to redo all of your iChat contacts.
Thereafter you can have FaceTime, iChat, and Skype all running at the same time with no issues.
This little trick did in fact resolve the issue for me. If you have this issue, try those simple instructions before you go deleting plists, etc.