In my last post concerning this mini-saga, I was in a dither because I now had a snappy display but no audio through the HDMI connection to our TV. Ugh. I did muck about with some command-line Linux stuff and this thread was actually very helpful, but was not the ultimate solution in my case. I confess I weakened for a time, and did consider just bypassing the HDMI cable and using some computer speakers for audio. I also thought about loading up Windows instead and running the XBMC application that way.
However, the final solution was pretty straightforward, and I did want to stay with the Linux-based XBMCbuntu for a few reasons; Linux works well on older hardware, and I feel it's quite a stable platform once it's configured. Also, the XBMCbuntu setup is built for the specific purpose of running the Media Center application, and it works well as far as I have seen.
My fix for the audio issue ultimately turned out to be as simple as removing a second sound card from the computer, and reloading XBMCbuntu so it could detect and configure the onboard sound card properly. Reloading only took about 15 mins or so, so that was not a big chore. I'm not even sure why the computer had a second sound card in it in the first place, as the on board sound worked fine. That streamlining of the hardware allowed things to work as expected; I now have smooth video and good audio on the big TV, both from a single HDMI connection.