|Go a little further with the shutdown - do this:|
Turn off computer, unplug power cord. Hold the Power Off/On button for at least 20 seconds to discharge the motherboard components.
It's a long shot but has been known to "unstick" things at times.
If that doesn't help let us have the desktop model number and tell us if you see anything at all on the screen when powering on.
Always pop back and let us know the outcome - thanks