The other one is most likely for the video card's sound. That is the one I was saying to try to disable before
Your drivers are newer. Mine are from a system built years back(never updated them).
This is very strange that it would not detect your speaker connected. I have never seen this outside of having basic Windows drivers, but with the ones from the Asus site you should have everything you need.
For the hell of it, try connecting the speakers to the BLACK jack on the sound card and see if it does anything.
If you swap from HDMI to DVI or another connector, does the audio work?
Do you have a folder c : \ program files \ realtek \ audio \ hda \ with a RAVCPL64.exe? That should be the control panel I was using. It downloaded your drivers and it is a part of the package for sure.