I just bought Fallout 1 today: download was fine, passed the integrity check, launches up fine now (I did have the "error: cannot initialize video mode" but fixed it by rennaming ddraw.dll), but now if I try to skip the game intro (the one beginning with "Brian Fargo") the background turns green and locks up. Even if I don't try to skip the intro and let it run, as soon as it's over the game freezes and shows a hippy-rainbow-coloured, pixelated vault door screen - I don't even get to the main menu.
Win XP SP2 (virtual machine run via Parallels Desktop; host is Mac OS X 10.4.11). ATI Radeon x1600 GC in host OS.
I have tried to re-download from GOG already. Nothing else is running.
I think this link should help you with your display problems, and I think it may help you with the game not starting up properly too. There are several different methods that seem to work.