This has nothing to do with PrivateFirewall, confirmed by the fact that I uninstalled the firewall completely, including all leftover files, rebooted and the problem was the same, only I found out that outgoing mail is also blocked. Yes, this has worked fine for a long time and something obviously changed, most likely with an avast update. Everything was checked and verified, including port settings, with my ISP techies, who are very well qualified and helped me much over the years. My accounts do not use SSL.
The server responded with an error. Account: 'promail.ptd.net', Server: 'promail.ptd.net', Protocol: POP3, Server Response: '-ERR , Port: 110, Secure(SSL): No, Server Error: 0x800CCC90, Error Number: 0x800CCC90
The bare fact remains: I must disable the web shield to send or receive mail.
Thank you for the help.