I recently build a custom budget-friendly PC but had some issues with the video output. The HDMI works only at UEFI/BIOS but, as soon as Windows starts, my monitor doesn't pickup a HDMI signal. My only option is to use a VGA cable which outputs 1080p but feels low quality.
Sounds as though Windows doesn't have a driver for the GPU chip or card that has the HDMI output. Go to Control Panel>Device Manager and look for the display adapter and click on Update Driver. You should also be able to find it at Radeon's website.