A tale of 2 ports. I was wrong! My settings were never set correctly. Everything was right except the outgoing mail port number.
I finally found that there are 2 port settings for my Mac mail and I thought in the past I have never configured but 1. Probably basic knowledge for a true Mac person but my last Mac computer was purchased 10 years ago.
Verizon has my incoming mail port setting 995 and the outgoing a different number. I never knew that. It's not obvious when going through the setup based on an older computers settings. I believe the Mac software on my old computer found the other outgoing mail port number for me but not this time with Mountain Lion and Verizon. Not real sure of that assumption on my part.
On Verizon's site there is a step-by-step setup for each individual customer's phone number. Thank you Frank for your Reply! I hope this may help other new Mac owners.