The DirectX installer that comes with the game could actually be causing the problem if the one you installed when you got the Demo is newer (which it likely was) because, when Civ5 installs it through it's installer it does so with the /fs (forced, silent) switches meaning it can in some cases cause incorrect .dll registrations. I would suggest installing the latest
DirectX 9.0c end-user runtime and seeing if this fixes the problem.