There's quite a few solutions to this out there but lets see if we can find the one working for you!
Since the error popping up mentions the 33165 driver which is from 2013 my guess is that you have a conflict with your Nvidia drivers / Nvidia settings. For this a clean reinstall of the latest drivers should fix it. To do this I would suggest using the Nvidia uninstaller and then using Display Driver uninstaller to clean up the rest, the download of this tool and it's usage is located here:
http://www.guru3d.com/files-details/display-driver-uninstaller-download.html
I know you said you already did this "correctly" but as I have no idea what you find to be correct and you are not specific I'll have to suggest it again.
Also, make sure to repair the game in Origin and then reinstall directx from the installer located in BF4's installation directory.