One other question that's occurred to me. When you updated your DirectX, did you download it from Microsoft or did you just get d3dx9_37 (or whatever) from dllfiles or somewhere similar? Or have you ever downloaded a missing DirectX file from one of these sites? Not just for DirectQ, but for Fallout 3 or any other game?
I ask this because it's obvious that the problem you have is either with the depth buffer or with matrix transforms. We seem to have ruled out the depth buffer, and DirectQ uses functions from the D3DX library for matrix transforms. If you have an "unofficial" version of one of the D3DX DLLs then I can't legislate for what that version might or might not be doing.
Even if you haven't I would advise that you update your DirectX again. This time,
before updating, go to C:\Windows\system32 and either delete the d3dx9_*.dll files or move them to somewhere else. Then go to
http://www.microsoft.com/directx and use the websetup to download and install the files you're missing.
Let me know how that goes.
WHAT I NOW BELIEVE IS HAPPENING
A 3D co-ordinate system can be either right-handed or left-handed (there are other systems too, but let's ignore them for now). OpenGL by default uses RH, Direct3D by default uses LH. Direct3D does also provide functions to use a RH system if you want, and DirectQ uses them to avoid messing with the base data.
Something on your machine does not like this. Either you have a bad driver, a bad installation of Direct3D or a bad installation of D3DX. It's not using the RH system at all, despite having been told to do so, and despite it being a required part of Direct3D.
So, let's start with seeing if D3DX is the cause, get that to a known and verified state, and work from there.