Possible Working Solution for Battlefield 4 Not launching Through Steam.
So when I bought BF 4 when it was released on Steam It worked, I uninstalled it so I could make some room on my PC, This year I reinstalled it and it wouldn't launch on steam, but as of today I might have found a solution, these are the steps I did to make it launch. Make sure you do this in order, last one being the last resort.
1. Uninstall Origin and let Steam install Origin
2. reinstall BF4
3. If you have GOG galaxy exit the program and make sure its not running in the background
4.Make sure Origin is not running in the background. Open the Steam Launcher, open up settings, go to downloads, click on Steam Library Folders, right click the folder where your bf 4 is installed, and remove library folder and then add it back again, then lastly open p origin and see if bf 4 is playable.
Now these ones are the last options you should do, do them with caution
5. Unlink your steam from origin and then relink them, bare in mind you wont be able to unllink for a long time
6. factory reset your PC
Hope this help,