Anotak and Kappes - thank you both very much for your inputs.
I already had DB2 installed, and had the same problem there. I had also tried installing DirectX 9.0c components via the web installer, but it kept tellling me that I was already running a newer or equivalent version.
After some "playing around" to find a solution, I ended up copying D3DX9_43.dll directly into the DB2 / DBX folder, and then it works! This file must have been corrupt in my system or something.
Now back to mapping! :D