Tried the d3d9.dll solution from nexusmods, and it just made the crash occur sooner.

I've tried compatibility mode, run as admin, reinstalling codecs, verified and reinstalled... Nothing works.

Fallout New Vegas is running fine.

Any ideas?

It's your Intel integrated graphics. FO3 won't run with it. There is a solution that sometimes works for some, but not all. Look for the Intel bypass. Best solution though is to get a dedicated graphics card.

Yeah, I tried the bypass, that's the d3d9.dll that didn't work. (Actually made the crash occur before I got to "New Game".)

I've also tried downloading the standalone installer and running it, noticed this oddity:

Microsoft Visual C++ 2005 redistributable tried to install to the wrong drive (an empty DVD drive) and so reported that it didn't have enough space. Cancelled that part of the installation, but the Fallout 3 installer in the end said it installed successfully. Wonder if the failed package is part of the crash issue.

I don't mean to sound cruel but the GOG page for Fallout 3 has a warning it does not support Intel HD processors.
Quite a few games don't. If you are going to play a lot of games, get a dedicated graphics card.

I also had the same problem as the original poster, that file did not work....

However, the trick I found at the below forum did!

https://software.intel.com/en-us/forums/user-community-for-visual-computing/topic/288710

There is also a threading bug in the game engine that causes problems on system that support >2 threads (e.g. ILK with hyperthreading, also Core i5-750 and up). Workaround is:
Adding these 2 lines to Fallout.ini in Documents\\My Games\\Fallout3 under [General]
bUseThreadedAI=1
iNumHWThreads=2

It started crashing... but....

It seems to start reliably after doing all of the above, IF I start the game with the original execute file, rather than through GOG galaxy? It is weird, I will see if that keeps working.