I have just set-up HDMI on my machine which I use with my television. I used HDMI because my TV, whilst having vga-in, did not have a mini sound jack-in. So, HDMI was the only solution to get sound and video in together. However, when I first connected it up, I too got no sound.
What you have to do, with the HDMI cable already connected, is go to sound preferences/output:
As you can see, from my screen-shot, HDMI is not listed. However, this is because I am writing from my laptop. On my machine connected to my TV (as with yours) I have the HDMI cable connected and so it will appear as an output option. You just need to select it and then close
That's it. you should now find HDMi is ouputting sound as well as video