Do you get an error message when you try to talk in group chat? Is it the same error you get if you try and talk in the General channel?
Have you done the starting planets Tython - Korriban - Hutta - Ord Mantel ? If not try that and also work your way up to where you actually get your ship given to you and see if that works. "Also here is a little cheaters tip you can use to get you by when your in group and trying to talk to another player type /e MESSAGE this is what the role players use to blab in the open chat but any one around you can read what your saying and then they can reply to you in the regular chat. Do this till you can figure out a way to get your restrictions fixed or if that's why you getting blocked due to not doing the starting planets and getting your ship the real way. If your on the Satele Shan Server look me up my Charater name is Warchildvolk. I hope this help and also fixes your issue. I am not a EA/BioWare worker eather im just a gamer.