I had a similar problem going on. Turns out it was processor. My screen would do more of a flash, but the same redraw looking line came up. I would suggest dusting your computer off, and looking at the heatsync, processor fan, and processor for any collection of dust. Dust on the heatsync (on the top side of the processor) is a horid- horid thing.

If you start getting a BSOD (blue screen of death) that does not point to any memory adress, or a fake one (all zeros) then I would say it is your processor overheating. Some motherboards supprt tools that will report the temeture (or will display the temp in your bios). If you can find the tem your precessor is running at, let us know what the temp is, and the type of processr (IE pentium 4 2.4 ghz, or pentium 4 HT 3.2 GHZ)

Try that out, if you want.

Bipper