Several readers of this site wrote to the Avast company and pointed them to my posting about the problem I was having cancelling my service with them and getting a refund for the portions of it which have never worked. At the same time, at the suggestion of a few of you, I posted a message on the Avast forum on Facebook.
I don't know which of these was responsible but this morning, I received a flurry of e-mails from Avast telling me how to cancel and get money back. Thanks to all of you for your help.