I gave up and moved over to another computer we have in the house. Seems to be working great with it's built in Radeon card.
I did some additional browsing this morning and didn't come up with a solution, but encountered a lot of others who had problems with the 8400 GS on older games. It is...
I updated to the most recent drivers and the problem persists. (Ironically, the lines appeared on the splash screen for the driver update program!) It looks like this is a fairly common problem with older games with the Nvidia GeForce 8400 GS. I've done a bit of searching but haven't found any...
I am having this issue as well with my original Interplay copy of Fallout 1. I have tried it with the original 1.0 install, the 1.1 patch, as well as the various unofficial TeamX patches. I have also installed the "Mash" High Resolution patch 4.0.2.
I am running Windows XP on a Pentium 4...