I didn't get an HDMI cord from Microsoft, but I still have the big grey plug that has a "TV/HDTV" switch on it -- don't know the name of it. How do I shut off HDMI audio and still have audio if the HDMI cord is the only cord that's connected to the 360?
The adapter you are talking about probably won't work at the same time as the HDMI cable, it is too fat. Is your TV 1080p or less? Because if it is less, there is minimal difference between using HDMI and the component video adapter (I am assuming that is what you have - Red/Green/Blue RCA connectors plus a red and white for stereo audio?) for the Xbox. HDMI is the only cable that has the bandwidth for 1080p, but component video will do up to 1080i.
For that matter, how do I shut off HDMI audio to begin with?
There is surely a menu option in your TV to shut off audio from HDMI, or select a different audio source for that particular video source.
If you still really want to have HDMI, you really should buy the Microsoft HDMI adapter because it can do non-HDMI audio. The only other way to do it is to butcher your other adapter - not a good idea IMO.
http://www.amazon.com/Xbox-360-HDMI-AV-Cable/dp/B000UODATY/ref=pd_bbs_sr_1?ie=UTF8&s=electronics&qid=1228847673&sr=8-1
And most confusing of all, why the f##k don't my DVDs skip the same way when I connect my upconverting DVD player to the same TV via HDMI? Argh.
That I cannot answer. Digital things are tricky. It is possible your HDMI port is a very old revision that is not 100% compatible. It is possible the frequency/noise floor/error correction/something else of the digital audio output on the Xbox is just not communicating with your particular port.
Hope I helped some. Good luck.
EDIT: If you are really handy you could butcher your other adapter to work with an HDMI cable. There are DIY guides on doing this; it will require a Dremel and a steady hand. At $42 for the adapter from amazon, you can decide. I personally think the $42 would be well spent, I don't like the looks of butchered plastic, even if it is at the back of my Xbox.