Thank you, Jason. I did try all those options. I also spent about 2 hours on the phone with Apple Care and they couldn't solve the problem. Finally, I exported all my mail boxes as a precaution. Deleted all my accounts and reinstalled them using the original settings and passwords. Everything seemed to be in order. Tonight the app informed me it could not connect to the servers. I rebooted my machine and things are working again.
The oddest component of all this is the ability to send emails from the iPhone, the iPad, and the web sites for the accounts just not from the MacBook Pro. It just seems logical that it is an application problem, not a server problem. But thanks for your advice.