I forgot who told me but I had this problem and I did this and it worked. Click the link and download the file and it should fix your problem.
Originally posted by another user
Ok we are getting a few messages regarding people receiving and error when trying to loadd up the call of duty world at war demo
d3dx9_37.dll was not found)
This error is caused by missing directx files, or in our case and older version of the file has overwritten a newer file which is causing an incompatibility issue, To fix This problem you simply need to update your DirectX version.. You can update your DirectX by downloading & running this tool. This will solve your Call of Duty World at War error message when trying to start the pc demo.