DirectX Error

It may not say direct x what you do is go into BF4 let it crash then go into event viewer error area and look at all errors at the time BF4  crashed. Edit....  kk let me look at what you posted.... Edit 2 ok its from the video card driver :/ Ok lets try and fix this puppy 

Get new video card diver or beta on desktop we need to get you a fully clean install of it after steps below.

So what I need you to do download CC cleaner the free version and install CC cleaner on your PC.
http://www.piriform.com/ccleaner/download

Remove the video card driver using the tools area of CC cleaner then reboot the PC.

When windows loads it will install a driver thats normal no big issue, once back on desk top then open CC cleaner again.This time go to the registry area and scan for issues , then pick fix selected issues it will give you the choice to do a back up. Then pick fix all selected issues you may have a ton of issues if you never have used this before its normal. Then reboot your PC again and do all the registry steps again until it finds none. Reboot your PC after you do each scan on registry. Once it finds none then move to the next step.

Now install the video card driver new one or beta

Next test bf4 if you still have issue ....

Try repair game or do this step again as the BF4 cfg could be messed up.......

BF4 folder in my documents holds game configs and screen shots even if BF4 is installed on different drive. When you uninstall BF4 it does NOT remove this folder. So when you install the game again you can still have the same issues.

1- Go to my Documents and remove BF4 folder place it on your Desktop or trash.
2- Be warned you do have to set up your in game settings again.
3-Repair BF4
4- When done go test your game.

Now test BF4 again