Occasionally I've noticed on a restart that audio doesn't work for me, but I've fixed that be re-enabling the audio device. Basically sometimes Windows will not get the audio stuff started correctly, but it's not hard to fix. Restarting the Windows Audio service has worked, as has changing the audio device. That being said though, I'm running through the speakers port and not HDMI, so things may be different.
First thing I would recommend you doing, if what I mention above doesn't help, is watching the volume mixer or playback devices menu (your second image) while playing some audio file. We want to make sure Windows thinks it should be making some noise. You should also try connecting headphones or more traditional speakers so we can know if it is all audio or just HDMI audio that is a problem, but that would be a different step than just testing for any playback.
Something else I've just remember is that you can Right-Click in the audio devices window to have it show disabled and disconnected devices. Perhaps that option you can't remember is there after all, but not visible.
Processor: AMD A10-5800K @ 4.40 GHz (44.0x100)
Cooling: Corsair H110
Motherboard: ASUS F2A85-M PRO
GPU: NVIDIA GTX 980 4 GB
PhysX: EVGA GTX 770 2 GB
Memory: G.Skill Ripjaws 4x8 GB (32 GB total) at 1866 MHz 10-10-10-27
PSU: OCZ Fata1ty 750 W
OS: Windows 10 Pro 64-bit
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