Thanks to some recommendations from a friend and some good prices, there's now a new motherboard and video card in Siobhan's computer, currently churning through installing device drivers. We were able to skip the "cheap temporary stopgap video card" approach and go right to the "final" approach.
Not only does it seem to be working, some things I never got working on the old one (like the front USB ports and floppy drive) seem to be working again. I had to rearrange a few drives to make everything fit but otherwise it was pretty easy. The documentation was great.
During the previous changes we replaced, one part at a time, every single piece of the system except the floppy drive and the drive cables. The drive cables have now been replaced, so the floppy drive is the only remaining part of the previous computer, even though there was never a time that the whole system was being replaced.
Only took me about three hours to get the new motherboard installed and working. Wonder how long the device drivers will take. Can't wait to see how good the performance is.