Hello slunday5,
Thanks for visiting Apple Support Communities. We understand that after transferring data from your old Mac to your new that you're unable to access your email in the Mail app. If you haven't already, remove the email accounts and add them back to see if that helps: Add or remove email accounts in Mail on Mac
If the issue continues, to help narrow this down, let's see what happens in safe mode and a new user account. Safe mode will let us know if a third-party app is causing this to happen. Here's more information on safe mode and how to start there: How to use safe mode on your Mac
After noting the results, restart to exit safe mode. If you were able to open and access your email in safe mode, after restarting, see if you're then able to access it when outside of safe mode. If not, create another user account as this will tell us if the issue is system-wide or only in your user account: Set up users, guests, and groups on Mac
Keep us posted.
Take care.