This PC is a laptop? If so I presume that the normal laptop screen is working?
Many laptops have a button that cycles between laptop screen, external screen and both. My Lenovo has that and I suspect it overrides any W10 software switch. FWIW there is no difference between a TV connected HDMI and a PC monitor connected HDMI. So it MAY BE that the W10 graphics driver on the machine needs a tweak, right click on the screen or looking at device manager or Advanced Display Settings in Settings-> display. Maybe this laptop thinks the TV is Display 2
I don't have a hardware set up to test this.