Hello Benjamin Haukaas
Can you please confirm if your Windows 10 is not a pirated version and is activated?
If it is genuine and activated, you can:
> Open the Run command box (press Windows + R keys together).
> In the available field, type explorer shell:::{D555645E-D4F8-4C29-A827-D93C859C4F2A}\pageEasierToSee and press Enter.
> From the Make the computer easier to see window, under the Make things on the screen easier to see section, uncheck the Remove background images (where available) checkbox.
> Click OK when done and restart the PC.
> Try changing the background this time.
If the above method fails, you can try the following:
> Open the Run command prompt.
> In the available field, type REGEDIT and hit Enter.
> From the opened Registry Editor window, from the left pane, locate HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Policies.
> Once located, expand the Policies key. *
> From the displayed tree, right-click ActiveDesktop and click Delete from the context menu. (Provide your consent to continue whenever and wherever prompted.) *
> After this, click to select the System key from under the Policies tree again. *
> From the right pane, right-click the Wallpaper string and click Delete from the context menu. (Provide your consent to continue whenever and wherever prompted.) *
> Follow all the above steps marked with * for the HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Policies and HKEY_USERS\.Default\Software\Microsoft\Windows\CurrentVersion\Policies keys as well.
> Once done, restart your computer and try setting the wallpaper.
Hope this helps.
Cheers!!