EDIT: Problem solved, was very simple. Installed DirectX from another game installer. Mods, please delete this thread.

I think it's part of DirectX so I would try reinstalling that, unless you've tried that already.

From Microsoft's website:

Install DirectX End-User Runtime if your application or game requires an earlier version of DirectX

Some applications and games require DirectX 9. However, your computer includes a more recent version of DirectX. If you install and then run an application or game that requires DirectX 9, you might receive an error message such as "The program can't start because d3dx9_35.dll is missing from your computer. Try reinstalling the program to fix this problem."

To resolve this issue, go to the following Microsoft website to install DirectX End-User Runtime:

DirectX End-User Runtime Web Installer

Note When you run this package, no change is made to your version of DirectX, Direct3D 9, Direct3D 10.x, Direct3D 11.x, DirectInput, DirectSound, DirectPlay, DirectShow, or DirectMusic.

If you experience issues in which an application fails because any of the following files are missing, you may be able to resolve the failure by running the DirectX run-time package:
...
XINPUT1_3.DLL
---

Install this thingy, then try again.

X Input has something to do with Direct X and the control input (XBox Pad, mouse, keyboard etc)

I would try downloading Direct X from the internet and re installing it again.

http://www.microsoft.com/en-us/download/details.aspx?id=35

A problem with your Direct X setup apparently

solution : Reinstall Direct X , I guess; Or find the missing dll and add it to the game folder

see also

http://pcsupport.about.com/od/findbyerrormessage/a/xinput1_3-dll-not-found-missing-error.htm

Do you get pop-ups during the install telling you it's installing something? They might be blocked by the UAC.