Run a sfc /scannow
to see if it may be able to find and repair any bad or corrupted system files that may be causing this.
If that does not help, then as a test, try specifying the wallpaper you want to use with the tutorial below to see if it will change it afterwards. Desktop Background - Specify and Prevent Change
As an alternative test to the specifying one above, create a new administrator account to see if you are able to change the desktop background in it.