I have finally found how to turn the TiVo off. At the bottom of the "Messages & Settings" screen there is "Standby". This switches off the video output, while keeping recording going. As there is no video, my LCD monitor then goes to sleep as well, saving power. However, it would be a lot easier if there was an "off" button on the remote control. I suspect the standby mode was put in just to comply with US Energy Star requirements.
I had a message from the people doing the TiVo registration web site (they saw my blog posting). They are looking at the problems I had with registration. But I told them I had found a workaround in the interim.
I mentioned the TiVo to two people, but gave up after that. The response was so enthusiastic it was a little frightening. In both chases the person claimed their spouse wanted one.