A:Answer OK - update. The guy at Best Buy was great - totally understood the problem and we discussed possible solutions. He suggested reinstalling the sound card driver (Realtec HD), which I did, and it didn't help.
It turns out that the HP Pavilion Elite (410y) has a quirk that's documented - if there's an external (well, not embedded) sound card it will disable the embedded Realtec sound card. Period. And it seems the Radeon RX 560 graphics card kinda looks like a sound card to the motherboard firmware, since it's capable of driving audio over HDMI (and DP too). So, adding another sound card is in order, unless I can find a way to disable the sound card features on the graphics card. Googling for advice now...