have you tried a different mouse? com/ps2? So is windows locked up or just mouse is locked up? You can do everything with a keyboard i think (not very comfortable but at least to check whether everything is ok).

I guess you had riva 128 and voodoo 3 in that win98 installed eariler? And maybe some other stuff too.
Remove that drivers from add/remove programes
run in safe mode and remove that drivers from device manager
also remove all other drivers from add/remove programes
and in safe mode remove every single device from device manager and let windows redetect them after a reboot.

I can uninstall the Voodoo 3 drivers no problem, but since I'm using dual monitoring with the Riva128, that needs to stay. I doubt that will fix anything, but I can give it a try.

Also, the problems don't originate from the mouse. As Windows is loading, all I get to see is the Desktop background, not the icons or the start bar. It freezes before I get to that.

The first thing should be make card work at all. So simplest configuration possible. Later you can try adding whatever you want one by one to figure out the problem. (Including different gfx cards if riva doesn't want to work with it).
It may be even your too modern motherboard that just won't work with this card. Or just anything else...

I think it might have some conflicting issues with AGP. Since I already have an AGP card installed, I might have to use this as a single card solution. Since syschk doesn't ignore AGP as a PCI-PCI bridge, that might be part of the problem. Second, I can't seem to uninstall the 3Dfx drivers from safe mode. Every time I go into safe mode, it keeps telling me that it sees the card as a 3Dfx Voodoo 3, which is not the case. Now the next question is how to get rid of those 3Dfx drivers!

in safe mode you can remove EVERY SINGLE device (including pc speaker, system timer, system board, etc... EVERY SINGLE DEVICE, EVERYTHING, so you will have absolutely NOTHING there, empty box) and that is what you should do.
Also have you removed all drivers/control pannels from "add/remove programs"?