Hi James,
Since you transferred the website from one host to another, I’m guessing there might be an issue with the Gravity Forms Notification settings. Check if the value entered in the “From Email” field of the Notification setting is using an Emai Address within the current domain. You may want to try entering the {admin_email} merge tag, as the From Email, to see if that works for you.
Also, you can check the Sending Result Notes within the Entry page to confirm if this is an issue with Gravity Forms or Godaddy. Here is a Gravity Forms Documentation on Troubleshooting Notifications with additional information, that could help you resolve this issue.
I hope this helps.