I am sure they are plotting against us all!
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As I understand it, you get no error message or anything, correct? Yet installing DirectX10 solves it...
Did you update your video drivers?
When the game hangs again, try this. Go to task manager, kill explorer.exe. then ell icons on your desktop and your start menu and everything vanishes. Click on file - or at least the option in the upper left corner of task manager, not sure on the english name - and select the first option. Type 'explorer.exe'
Now everything is back in place the way you left it, Try to run Civ. Does is work then?