Crashing when running dxdiag is not a good sign. The problem may lie with DirectX, your display driver, or the display card itself. Have you upgraded your display driver lately? Particularly Nvidia drivers are in my experience often buggy (the main reason why I've changed to only use ATI cards).

There is also a procedure that you can follow with a tool to remove DirectX to be able to reinstall it from scratch (it won't ever let you downgrade any component), but it's fraught with danger if you do something wrong, meaning you'll probably have to reinstall Windows if you screw up. I did this procedure lots of times when I was troubleshooting an Nvidia card back in the day, but I can't remember the tool I used. I'm sure you can find it with Google.