Seeing as this turned out to be a probable hardware issue, I moved the thread to the appropriate forum.
I did just recently switch from the PCI video back to the integrated ATI video, which I had been intending to do since shortly after switching to the PCI. The mobo/bios apparently has issue with ignoring the integrated graphics when a second card is added. I tried two different cards in this machine, and both of them had trouble with both 2D and 3D acceleration...the Geforce6/256 performance was worse than I used to get with a Geforce2/64. Granted that's comparing PCI with AGP, but still the Geforce6 shouldn't be anywhere near that bad. 2D acceleration is much better now with the integrated video -- 3D acceleration is non-existent with the available drivers, but at least I can play fullscreen video again -- so it will do until I switch systems. It may be the source of this ghosting, though.
The next system waiting to be installed isn't a big improvement in terms of the basic specs (same p4 3ghz processor, 1gb ram as opposed to 512mb), but it's a custom build rather than the assembly line HP I'm using now. Still going to be using the PCI video, though, until I find a decent AGP nvidia card (no PCI-e on the board, and I still have no faith in the ATI Linux drivers). Who knows, though...the PCI card might turn out to be adequate considering I have no interest in cutting-edge gaming. As long as I can do some sculpting and video in Blender and occasionally load UT I'll be happy.
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/ >) My 84-year-old non-techy mom uses Debian Linux. It ain't that hard.