Ok, when using a phone cord, the remote found the TIU again and worked fine with trains. Our other remote would not work as long as the broken remote was connected to the TIU with the phone cord. I disconnected the broken remote from the TIU and tried to send a start-up command wirelessly. We got an out of RF range message. A few seconds later the train responded to the command sent by the broken remote. We then sent a shut-down command to the same train with the broken remote and it shut down immediately, but no more wireless commands worked When sent from the broken remote.
So, it seems to me the broken remote is working, but it is not functioning wirelessly. I'd be happy to leave the broken remote hooked up with a phone cord, but then our other remote will not communicate with the TIU. What should I try next?