I've got a computer that runs Minecraft without problem, and a couple of others that don't even let me try because of "bad video card drivers". The cards are too old -- updating drivers doesn't fix the problem. Is there a way to override this check that Minecraft does? Would a remote-desktop solution be plausible?
I believe that it requires hardware-accelerated OpenGL with driver extensions to support it. If one of those computers has an Intel graphics chipset, installing the Intel version instead of the built-in Windows one usually fixes it.
Rage128 only supports OpenGL 1.2, but Minecraft requires 2.0. It just won't work with that card, sorry.
Try the In-Browser version... I get the same issues on one of my computer's but the In-Browser version works ok.