were you ever able to play these 3D games with this riva 16MB card? because i would think 16MB is not enough memory to display the game correctly, which is why you could be having problems.
in software mode the game is using your CPU as the source to render the objects. that CPU is probably doing a better job than your video card would have with full hardware support i think.
just bear it out and wait until you can buy a new card. why do you have to buy top of the line? a fx5600 or ATI radeon 9600 would still be good. i don't think you need to spend more than $130 for a video card. here's a link: