Can't access saved emails on Mac

Can't access saved emails on Mac. I have not been updating the operating system on my Mac because I have old programs that I need to be able to keep using (which will lose functionality if I update), this is fine because I have another computer that I keep updated and can use. The problem is that my older Mac is the one that I would pull in my emails to Mail. I saved A LOT of emails for future reference. One day, I could not open Mail. It wanted me to set up an account by connecting a webmail account. As soon as I hit the button without connecting a new email account, Mail quits. I don't need it to pull in new emails. All I want to do is to be able to access all of the saved emails on my Mac mail. Is there a way I can get to them on my Mac, somewhere? Thanks