No audio through HDMI connection [on hold]

Background

I'm able to use my HDMI connection to show video for movies, but the audio still wants to play through my computer's speakers rather than the TV speakers.

Ordinarily, I would visit Control Panel -> Sound, and set HDMI Audio as the default sound device.

Unfortunately, no such device was listed. After updating my audio drivers, I was able to get the HDMI audio device to at least show up. At this point, most tutorials online indicate 100% success.

Summary

In my case, the options Set as Default, Test, and Configure are all grayed out, and it says not plugged in. No online tutorial is of any help, since they address only the earlier problem.

Steps taken to attempt mitigation

I have uninstalled, reinstalled, and updated my audio drivers.

I have updated my nVidia drivers.

I have updated and restarted Windows.

I have restarted my HDTV.

I have swapped between several proven good HDMI cables.

I have configured my HDTV for digital (PC) input.

I was not able to find any HDMI or audio settings in BIOS other than UnLock/Lock--and it is indeed unlocked.

I was not able to find any HDMI or audio settings in the nVidia Control Panel, just the 3D and PhysX tabs.

I was not able to find any HDMI or audio settings in the Intel Integrated Graphics control panel.

No luck.

System Specs

I'm using Windows 8.1, on an ASUS N56JN laptop, with an LG HDTV.