I've tried to locate the d3dx9d_33.dll file on my home pc, but I couldn't find it.

I've done some more digging and it appears that d3dx9d_33.dll is a debug version developers can use it to, well, debug their applications. Once a stable version is reached it is possible to compile to a version that requires d3dx9_33.dll to run. That file however is available on any normal DirectX installation.

From what I understand, (but haven't tested yet), I could install the DirectX SDK (+500mb) which comes with the necessary dll's and also a Control Panel which allows me to set the option to switch to debug or release. Apparently it is also possible to download the Control Panel separately , but sadly in my case many options were disabled, including the one to switch between debug and release.

For the moment I'm going to assume this is a necessary step to continue. Although it still does not explain why I my home installation has no issues, while the setup at work does.