Configuring the SMTP plugin worked for me, as suggested by jenyus ...
I am on DreamHost shared hosting ..
I use my own child theme of the Twenty Ten theme ..
I set SMTP host to be 'mail.mydomain.com' rather than 'localhost' .. this is a typical DreamHost setting ..
I supplied the username ("Use the whole thing!" right DreamHost :)) and password for my sending address .. 'info@mydomain.com'
And now it works! Thank you all. Good luck to the rest of you.