I have never used an HDMI connection to a TV (so I am just shooting in the dark), but I know HDMI includes video and audio signal, your tv probably does not have a built in DD decoder. Maybe the HDMI is overriding the fiber optic out to your receiver. Does the TV or D* receiver have some way of disabling the audio over HDMI, or is it automatically disabled when you hookup fiber optic cable? Maybe try another video cable such as DVI, component or S-video, just to see what happens. (Just a wild guess)
You said you don't get sound on OTA, does that mean that you do get sound when watching a satellite channel? I would think that if one worked then both would work, but I am not familiar with how the H10 gets OTA signal, on my HR10-250 it is seemless, do you have to switch some kind of inputs to get OTA on the H10?