Hmm...you were right to try to reinstall DirectX - that looks like it is the problem. Did you try installing the latest version (found here)? It should install over things, no problem.
I haven't played Call of Duty: World at War, so it could be specifically related to that game. Be sure to install the latest patch (here). If you're still not having any luck, try reinstalling the game. If it prompts to install DirectX, click 'yes'. If you're getting the 'DirectX is running' error across reboots, you might try reinstalling in safe mode to ensure there's nothing else running.
If you're still having troubles, type 'dxdiag' in the Vista search box in the start menu, click 'save all information' from the popup box, and paste the text from that file here.
Let me know if any of that works out.
--Andrew
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