After downloading FO4 from steam I tried running it and after hitting play the screen would go black for a moment then FO4 would close.

My fix.

To get it to work try going to your "Windows program compatability troubleshooter" located at Control Panel\System and Security\Action Center. click next to show the list of programs.. FO4 wasnt there for me. select the one that says "not listed"

on the browser navigate to your steam folder in program files, C:\Program Files (x86)\Steam\steamapps\common\Fallout this was my location. select the main program then run the compatability troubleshooter on it. use its fix. if its not that one then try the launcher on in the same spot. this worked for me! (the fix took me to windows 8, not 8.1

Hope this helps!