TDM in Windows 2000
Up to TDM 1.02 no special actions were necessary to download or run TDM in Windows 2000. With TDM 1.03 (and the added feature of built-in downloading capabilities) a few additional steps are required.
Updating / Installing
To run the TDM Updater in Windows 2000 you'll need to download the GDI+ redistributable which you can get for free from Microsoft. After download run the exe and specify a temporary folder where you want the files to be put into. The self-extractor will create a folder called asms\10\msft\windows\gdiplus in the target location, you'll find a file called gdiplus.dll in there. Copy that file to your c:\winnt\system32 folder (or you can try placing it next to your tdm_update.exe) and you should be able to run the tdm_update.exe without further issues (TDM 1.04 and upwards).
Special case for TDM 1.03
For TDM 1.03 (released December 2010) the updater will refuse to run at all in Windows 2000 due to a dependency on a Windows XP component. Please download this fixed updater instead and make sure the --noselfupdate option is checked when launching the updater (Advanced Options > Prevent updater from updating itself).
Fixed TDM Updater for Windows 2000: http://www.dramthethief.com/darkmod/files/win2k/tdm_update_w2k.7z
Starting The Dark Mod 1.03
The standard TDM 1.03 installation will refuse to start in Windows 2000. Please download a fixed tdm_game01.pk4 file and overwrite the one in your darkmod/ folder (note: you'll need to have successfully run the updater first).
Fixed TDM Game Pak: http://www.dramthethief.com/darkmod/files/win2k/tdm_game01.pk4
Note that the problem will be fixed in TDM 1.04, so you won't need a special tdm_game01.pk4 for TDM 1.04 and upwards.