Hello! Is it possible that there's more than one HD Audio controller in your PC? Like maybe there's one hidden in the GPU which isn't actually doing anything? Try running hdastat (available from
here) from DOS and see what card(s) it identifies…
EDIT: Just tried it myself and I'd forgotten how much output it spits out!

You can pipe the output to a text file and search for the text "found at bus/device/function". It may detect more than one device, or it may fail to detect any device (in which case I'm not sure what to do next…

).