Don't worry, I already fixed my (latest) prob. I'm just posting my fix for anyone else out there.
Was reinstalling Fallout 3 from GoG and was going crazy, because the black-screen-on-launch happened.

Tried a .dll fix. Tried to set FO3 executable as Administrator. Tried setting Compatibility Mode.
Each of these 'fixes', I had to get up from my comfy chair over and over because the game would blackscreen, and then I'd have to get up from my chair to turn off/restart my computer.

No mods or utilities installed at all, yet! -- However, at some point I discovered I could run the game in Windowed mode. HMm.
Was about to install the Anniversary Patcher when I just happened to notice that the Full Screen setting in the launcher was set at some resolution I don't use. Ah-ha! It should be 1360 x 768. Bang!! Now the game starts & runs. Phew.
It's just a reminder to myself and others: always check the small, easily-overlooked stuff too.
