Is it permissible to use on Shabbat the computer that has being left on from friday before Shabbat to talk during a video-conference?

It should not be done. The case is similar to using a microphone which is not allowed, in this case it is worse because of the picture. Participating will activate all sorts of electronic signals that should be left alone on Shabbat, although there is certainly room to discuss whether there is in fact a Torah prohibition.