OK, the problem is finally solved.
The story is as follows:-
First I got rid of the "from" address <firstname.lastname@example.org> that postfix was using that isn't a fully qualified domain name. I did this by adding an entry:
to the "sender_canonical" file in /etc/postfix.
There also needs to be an entry in main.cf in /etc/postfix like:
sender_canonical_maps = hash:/etc/postfix/sender_canonical
which tells postfix that the map is in sender_canonical. This entry was already there.
Once I did this and refreshed postfix, at least the mail logs started showing my email address as the "from" address. However I still
could not connect. I was getting the same error!!
[Now here comes the embarassing bit]:-
Then I thought - let me boot into NT, send an e-mail using Outlook express and see what the detailed headers look like. I did this and to my surprise I didn't see "smtphost.suffolk.lib.ny.us" anywhere in the headers. In other words OE wasn't using the mail server that I had thought it was using at all! In fact it was using hotmail servers and the hotmail servers had been set as default. So could the problem be with the .lib server?
So I set the default server back to the .lib server and voila - I could not
connect with OE. Then a memory came flooding back - Sometime last year I had changed the default e-mail account in OE to hotmail because .lib server had mysteriously stopped working. I had forgotten about it and all the time I thought that I was using the .lib server for SMTP. The reason it had stopped working was that my ISP (optimum online) had silently filtered out port 25 requests because of spam issues. But hotmail's account continued working because it is http based. So in fact I cannot use any e-mail server on port 25.
However I can
use optimum online's mail server on port 25. So I changed the smtp settings to mail.optonline.com and to my relief everything worked - and not a moment too soon.
Such was the manner in which an imminent nervous breakdown was prevented.
Thanks for your moral support :-)