Thanks for your response!
I followed directions and then some. Keychain First Aid found no problems via verify or repair. Close, restart, I continue to get the "mail can't connect to the account 'email@example.com'." Reboot = same result. I added the eMail address of firstname.lastname@example.org separated with a comma, same thing. The preferences indicate that the account(s) are offline, GMail works fine. The last eMail via my .mac addressed was downloaded on 3/3/13.
I opended Pacifist to try to extract the Mail application, failed. Oh no....