A lot of potential problems can be identified by looking at the warnings.log and dxdiag.txt.
Here's how you can find those files:
It is located in your Dawn of War root folder. If you installed Dawn of War to C:\Programs\THQ, it will be in C:\Programs\THQ\Dawn of War.
This file contains the result from your dx diagnosis tool. Run the tool by clicking on "Start", selecting "Run", and then typing "dxdiag", followed by enter.
A new window will open. Click on "save". The information from the tool will be saved in a file called dxdiag.txt.
Since those files can be rather lenghty, please surround them with code tags:
[code]<Your file goes here>[/code]