I had this issue with my game last night. To work around it, I simply saved the game where I was, exited to the main menu and reloaded. The game started operating normally for a turn or few, then would stop responding again. I went through this cycle about 5 to 10 times, then it stopped happening and I continued to play normally. Should have saved a save game to send in.
One of the last times it happened, I noticed that the move I had tried to make, seemed to occur a couple of minutes after it "stuck". I didn't try just letting the game sit for a few minutes. Maybe it was trying to work through something. : /