Well, after doing some additional research, it appears as if the S3 Prosavage DDR video card is certainly the issue (as evidenced by anyone who has that card and has posted here!). The Xfree driver "savage" gives buggy support for this built-in
card. VIA's site has some advice for several distributions (Debian and Slackware are notably absent) on how to get the drivers running properly, but it didn't look like much when I read it. S3's site only has windows drivers for the ProsavageDDR chipset. So, I took some advice from someone else who posted here with this card. I am now using the generic VESA driver, and now X seems to be running fine. I hope this helps someone else out there.