I don't know, because I had the resolution mod prior to updating my drivers. maybe for some reason I just needed to reboot after installing the resolution mod? doesn't make sense that I'd have to. but after installing the resolution mod and updating my drivers it did work, so try it his way, I know I did, and if it doesn't work, like it didn't in my situation, try updating your drivers.
I've tried every fix posted here and I get the same error even with the latest WHQL nvidia drivers in conjunction with the 1.2 hi res patch. It'll start OK without the hi res patch, but errors out with it installed. Help!
[EDIT] Renaming ddraw.dll fixed this issue!
The game works in 640x480 without the high res patch for me, but not with the patch. Renaming the ddraw.dll supplied with "GOG's Fallout" makes it work again.
I suspect the dll is there to make the game work with 640x480 on modern systems, as some cards cannot display graphics in that mode anymore. Someone with a better/newer computer than me would need to confirm this.
I suggest getting the high res patch and renaming the ddraw.dll file to ddraw.dll.orig or something, just in case. Read the patch's Readme file for install and config hints. I only needed to install it, then change resolution in the ini file to what I use. Uninstall is as simple as to rerun the patcher.