OK, Firstly, this issue is [censored], we've all been there, 30 different drivers, reinstalled 20 times, i just about lost a kilo of hair with stress, lol.
Secondly, my computer is not under-powered, please check the minimum specs before anything else. I have a i53330 @3.80GHz, 16GB ram, multiple SSDs, and a GTX 960 4GB.
Thirdly, I tried many "tips" to get it working first, including altering my ini which did nothing lol.

So, basically, right click the fallout 4 icon on your desktop, then go to properties.
Now, make sure that it isnt set to open as admin in the "compatibility" section.
Next thing to do is navigate to Documents (my documents on older systems) to find your "My Games" folder.
Find the folder named "Fallout 4" and delete it.

Open the game and enjoy... at least i did. Good luck and have fun guys