I have a Xbox 360 Premium version w/ the original component cable output (large trapezoid). I just bought a new LCD panel and would like to upgrade to a HDMI connection if at all possible. I see that M$ makes a HDMI adapter that will fit into the old output in my console. Can I expect this adapter to improve my picture quality vs. the original component cable? I've been told that the adapter changes the analog signal to digital, therefore reducing the PQ that you get in the end.

If you absolutely hate cable clutter and want a single cable going from 360 to the TV, or if you are short on component inputs and only have HDMI available, consider the converter. But what you heard about quality is likely true. Your new TV is a digital panel, and any incoming analog signal, it will convert to digital and upscale to its native resolution. If you get the dongle and connect via HDMI, you use dongle's circuitry for analog/digital and upscaling. And I'd bet TV's circuitry for doing that is superior to whatever that $90 dongle has.