Need some more information:
1. What EMail program are you using?
2. What exact Mac OS are you running?
3. When you say "old email address", is that an Email addressed "associated" with your ISP, or is it "connected" with gmail.com, hotmail.com, or yahoo.com? For example, I have two "primary" EMail addresses associated with my ISP, Comcast, and I access them through Outlook 2016. One of them is the one I use for about 98% of any correspondence I wish to receive. It is also the address I provide to banks, insurance companies, etc. I also have EMail "accounts" with gmail, hotmail, and yahoo. However, I only access them through my browser.