This could be due to Windows 7 themes. Try disabling aero in the system settings.

    -Start
    -Search for "Change the theme"
    -Use a basic theme without aero or create your own.

You should also make sure your game resolution is the same as the monitors native resolution.

Source:

I'm using dual monitors myself on basic theme while playing Arma III myself
and my desktop doesn't go black.

I think I understand what you're saying. You're trying to use 2xW for sprint correct?

I believe the issue is down to the fact that the sprint function requires you to be already moving in order to activate. Using 2xW you aren't moving already.

Toggling on/off sprint does not require you to be moving, it only changes the way you run once you do start moving.