Are you running the new account wizard? You'll need to decide what type of account you want, POP or IMAP, but not both.

Did you switch to manual setup?

https://support.mozilla.org/en-US/kb/manual-account-configuration

What are the server settings for Rogers, can you provide a link?

Thanks nfor helping christ1

I have the latest Thunderbird but I can find no wizard in the help or tools tab. When I tried to add account me@rogers.com, the message I had received from Rogers directed me to use IMAP port 993 with SSL enabled and SMTP port 465 with SSL enabled.

I had already viewed the link you provided and while I was able to stop the automatic setup and go to manual, the only options I had were the port numbers and SSL/TTS. I got an unable to connect message and was kicked off.

Am I missing something vital?

You start the wizard via File | New | Mail Account or via the Account Settings.

Using the manual setup, by selecting SSL/TLS for Connection Security you implicitly select the port numbers. You do not need to enter the port numbers manually this way.
Try again and make sure the settings are correct.

I repeated everything via the File | NEW | Mail Account and Manual Setting with the same error message "Thunderbird doesn't recognize Rogers settings". I added the account to my iPod and iPad with no difficulty. Rogers is connected with Yahoo now and I wonder if that is introducing the problem.

Great suggestion sfhowes! I now have the account showing in my inbox but when I sent a message to it I got a Thunderbird warning that the Rogers mail was not accepted. Go figure??

Well Thunderbird could not communicate with Rogers in the wizard, what would change now. Of course it will not work.

You have not identified or corrected the original issue,  which in all probability is your anti virus.  Nortons in particular, but almost all anti virus programs these days come with a firewall that blocks the communication process between Thunderbird and the server.  So check your firewall component and make sure Thunderbird has full access to all ports on the internet.

Then disable mail scanning in your anti virus program. Reboot and then see if it works.

Well Matt this may well be the problem I am encountering. I checked my AVG panel but quickly realized that I am not up to this level of technical competence. And I can't help wondering if I really want to disable my e-mail scanning and take a chance on viruses. If I want to get Rogers mail I think I am going to have to give up on Thunderbird.

Thanks everyone for the help.