First off, lets check if the device has been disabled or disconnected. You can do this by going to your taskbar, right-clicking the speaker icon, selecting your playback devices option. Under this window, you should see a few different devices. If the HDMI still isn't showing up, right click in a blank area in the devices boundary and ensure both "show disconnected devices" and "show disabled devices" are checked off.
If you do find the device after this step, all you need to do is right click it and select "enable device." If you don't find anything new, post back here and we can try a few other things.
Also, is this a laptop or desktop? What brand laptop, or if desktop, what are the specs?