Hey, a friend and I have just tried to get a multiplayer game going several times. With the same result every time. My mate cannot end his turn, so the game cannot progress.
We've tried several race combinations, on the theory that the seemingly unfixed problem with Terran Alliance causing the turn to hang was the issue. No such luck. The turn hangs regardless of who plays what. We're both using the latest drivers, the latest version of GalCiv3, and the same DLC (but then, without exactly the same DLC you cannot even start a multiplayer game at present, it seems).
I'm obviously slightly miffed we had to buy more DLC to be able to play together and then multiplayer doesn't work after all. And look forward to a fix and an explanation ASAP.