Thanks for your answer adlerpe. First, to answer your question about which cords I was using, I was using AV cords with the 3 plugs and the headjack hook-up. That was my mistake. I thought the ZuneHD could use just the AV cables.
Initially when I searched for connecting my Zune to a TV, the only models of Zune being shown to successfully hookup to a TV were older models that could use just the AV cords. Well I now know that that doesn't work for the newer Zune HD's.
Since then, I have ordered (and received) a Zune AV dock and the problem has been solved. So I have my dock and a HDMI cord and I'm in business.
Thanks again!