I have a 3dfx VooDoo 3 3000 and I have the official driver for W2K in a PIII 1Ghz with 512 MB of Ram. When i tried to play with UT 2003 Demo it refused to start.
My interest is to look how far can go my 3dfx Video Card because I don't want buy a nVidia card!

PLEASE help me!

Hm, that is quite odd...

Have you also applied the latest Patch for the Demo ?

The Patches for UT2003 and its Demo resolved quite a number of Problems with 3dfx Cards and this Game.

Normally, it should run.

(Check my early experiences with the unpatched Demo here :
http://www.falconfly-central.de/cgi-bin/yabb/YaBB.pl?board=games;action=display;num=1034382568 )
Things should run much better than that now.

Also, have a look at the 3rd Party Drivers. Some of the very latest Drivers were tested quite well with UT2003...

In case the Demo does not set the required settings in the UT2003.ini (to prevent or troubleshoot problems), you should have a look into it. Modifying the UT2003.ini (Direct3D Renderer Section) was always the Key to success in the Past.

PS.
I run it with an ATI Card, so no NVidia is needed anywhere with R8500, R9000(pro), R9500(pro) and 9700(pro) available to do the Job just fine ;D

Nonetheless, the Voodoo3 can do it , although not at record breaking Image Quality or Performance ;)

try to disable "geometry assist" in 3dfx tools ( sw t&l emulation ) i had problems with my v3 too, until i disabled the feature. i hope you understand me, my english is not so good.
what i mean: disabling this feature should make ut2003 run on a v3.