have you tried restarting from the help menu with add-ons disabled. weirdness like you describe is often caused by an add-on, particularly as the compose interface changed in the 3X. releases

Restart with add-ons disabled did not resolve this. Still need to copy or type email address into the To: field when I reply to an email.

Did the header of the original message show a reply-to address?

Actually, they indicate "From", not Reply To.

There should be both. My message headers have both. The message headers that I have are Subject, From, Reply-To, Date, and To.

OK. Looks like some do, some don't. The email of your response "There should be both. .....

From Mozilla Support Forum Subject finitarry posted an answer .... Reply to no-reply@mozilla.org To Me

Now, if I select Reply, I would expect Thunderbird to pass the "no-reply@mozilla.org" address to the new email (even if it were bogus); however, I get a "blank" To field on the new email. Curson focus is on the To field.

No idea what causes that. Thunderbird and SeaMonkey both put what I expect into the headers for both message and compose windows. I was unable to find a setting controlling that.

Bit of a long shot, but try restarting the operating system in safe mode with Networking. This loads only the very basics needed to start your computer while enabling an Internet connection. Click on your operating system for instructions on how to start in safe mode: Windows 8, Windows 7, Windows Vista, Windows XP, OSX

Sometimes better off to just reinstall that try to repair. After reinstall, works fine. Thanks everyone.