This text is directly from www.ttdpatch.com's FAQ, thanks to Kirill Krasnov for the tip
How do I run TTD/TTDPatch on Windows NT, 2000 or XP?
Only the Windows version of TTD works at this time. You have this version if you see the "Fish UK" logo at the title screen.
You need TTDPatch 1.8 or later
You need to enable the Windows 2000 patches. Simply put the line "win2k on" in the file ttdpatch.cfg.
If you have problems running the game fullscreen, or if you have no music/sound,
try setting ttdpatchw.exe (and/or TTD itself) to run in Windows 95 compatibility mode (see below).
For information on the compatibility mode in Windows 2000, read the related Microsoft support article.
If you get a message saying "Unable to access Transport Tycoon Deluxe CD! $", you forgot to tell TTDPatch to apply the Windows 2000 patches
(either run "ttdpatchw -2" or put "win2k on" in the configuration file.)
If you get the message, "Create process failed", you need to delete the file TTDLOADW.OVL and run TTDPatch again.
If you still get that message, try reinstalling TTD.
Detailed instructions for enabling Windows 95 compatibility mode on Windows 2000
Go to "Start", "Run", enter "regsvr32 C:\winnt\apppatch\slayerui.dll"
Go to the folder where the TTD is installed (e.g. C:\MPS\TTWin95\)
Find "ttdpatchw.exe" which you should have installed in this folder
Right click ttdpatchw.exe and select "Create shortcut" from the menu. This will make a shortcut of that file in the folder.
Right-click on the shortcut and select the "Compatability" tab at the top.
Tick the box next to "Run in compatibility mode:" with Windows 95 Compatibility Layer in the drop down menu box which should be default.
Move the shortcut to somewhere more convenient on your PC, e.g. your desktop
Note, you may have to adjust the path names in italics to your system configuration.
Some graphics cards do not seem to support TTD in fullscreen even after this procedure.
If that is the case for you, it may help to upgrade your graphics drivers and/or DirectX drivers.