I'll provide my system specs if anyone needs them, but I honestly don't think it's a hardware problem.
When I run Dark Forces II, everything runs fine except for the in-game display... the targeting crosshairs, along with the part of the character that shows (the hands/gun/saber area of the screen) appear out-of-sync and the scanlines are shifted out of whack, almost like a monitor whose display is messed up.
I know my description might not make much sense.... I'll take a screenshot if it's possible and post it if nobody understands.