Home Theatre & HDMI Applications

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So, I have this antiquated home theatre system that really needs to be replaced already. It still serves its purpose well but after coming from the home enrterainment shop, you realize, that what was wonderful years ago... well, has room for so much improvement. In turn, I've decided to do a little bit of reseaserch and move this along.

At this time, I am only concerned with sound. I will keep my TV and my Subwoofer and Klipsch speakers. The amplifier is an old Denon that has no HDMI support and decodes DTS-ES and older.

What I would like is a new system and I would love to get rid of all the wires. This is where my query begins. How do I utilize HDMI? I hear it carries both video and digital audio which is great! All I have is a DVD Player, an Amplifier, the speakers and the TV. No X-Box, PS3, DVR, etc.

Is it true? All I need is an HDMI cable from the DVD Player to the Amplifier and another HDMI Cable from the Amplifer to the TV? Can one of you gurus comfirm? If so, I should start looking around for an amp already and get two more surrounds.