I called the manufacturer today and their tech department got my iPod and the new theater system in sync.
It works, but is a bit of a pain in the butt. I can now hear my music, but I have to walk to the theater system, start the iPod manually, move through the menu to what I want, and then put it in the dock. My old one was mostly controlled by the remote for the theater system. Oh well. It's a small thing, I suppose. The guy who was helping me was a bit of a doofus, one of those who read everything from a scripted monologue, and when it didn't go exactly as his sheet told him, he didn't know quite what to do. I was smarter then him on that. The point is that it works now.
I'm not sure what I'm going to do with the old TV. I've been thinking about putting an ad on the community bulletin board, sort of a last-century version of Craig's list, and offering it free to anyone who will pick it up. It would make for a good TV for someone who can't spend what a new one costs. I think I might see if it works. Can't hurt!
Now I need to go set up the old theater system in my office. I'm so technologically fixed up I can hardly stand it!