I apparently wrote the right key words to trigger a response. The next day there was a message on our home answering machine waiting for me indicating that iRobot wanted to replace my Roomba, free of charge, as a courtesy. It wouldn't come with a battery however it's easy enough to swap them.
The replacement Roomba arrived yesterday and it works like a champ. Our floors will once again be cleaned by electronic means. Hurray for a bit of whining.