The hdmi spec requires digital audio support.
It's possible that you've run into our old friend and hdmi's dirty little secret - an arbitration error.
Those are sometimes hard to ring out and never make any sense and often appear as missing either picture or sound.
Believe it or not, I've seen this cured a number of times with a different cable - and if you can, try one half as long or twice as long as the one you have now.
Also - and I had this happen to me - look into the hdmi port on the TV with a STRONG light and if you need, a magnifying glass.
I had a no sound issue that was caused by one of the wires jumping the plastic tracks and shorting its neighbor.
I fixed it with a needle, patience and persuasion - TV off of course!