If all else fails, you can try the following:
- Uninstall UT2k4.
- Delete the UT2004 folder.
- Reinstall the game. Make sure to type in your CD-Key very carefully.
- Without installing/changing anything else, install Duffers Golf and see if that works. Like Mix said, make sure you unzip the .ZIP file into the UT2004 directory, and not into any subdirectory within.
If it still doesn't work, it's probably not a problem with the mod.
Another important note: do not install any UT2k4 Beta Patches that are floating around out there; many of them break mod support.