When I try to start the game I get a small black screen the collapses after a few seconds.

My system is an ASUS laptop with a Intel i7 4500U 1.8 - 2.4 gHz CPU, 8 GB RAM and a NVIDIA GT 745M Graphics card. I've tried updating drivers and verifying file integrity. Any suggestions?

Your hardware isn't good enough.

...obviously your laptop runs the game through the Intel HD GPU and not your Nvidia GT 745M, and therefore the crash!

You can check that:http://imgur.com/3BdgESZ

What's listed under sD3DDevice= ?

It does indeed say it runs through the Intel HD Graphics, but there is a NVIDIA driver or chip in there also, supposedly the device driver retains the performance of a NVIDIA GeForce GT 745 card.

You must force the application to use the nVidia graphics if it doesn't trigger the switch over properly.

https://knowledge.autodesk.com/support/infraworks-360/troubleshooting/caas/sfdcarticles/sfdcarticles/How-to-force-your-laptop-to-Run-with-Graphics-Processor-vs-the-default-Integrated-Graphics-for-InfraWorks.html

Switchable graphics is buggy and the bane of laptops and trying to game.

That being said, the GT 745M is really too weak to run Fallout 4. You are looking at under 30fps.

Try running at 1366x768 with low settings