At the risk of being redundant here goes:
Go to My Home
In the left most window find and click on Edit Options
Find the blue bar Messaging and Notifications
Under "Receive Email"
I would think you want to receive messages from Administrators so check that box.
Remove the check from Receive email from other members if you don't want to receive email from other members.
Check the Default Thread Subscription. Change to "Do not subscribe" or "No email notification"
Under "Private Messaging"
Enable Private Messaging - your choice to receive or not to receive. As far as I can tell this is the private messaging system on TBN.
Receive Private Messages only from Contacts and Moderators - your choice
Receive Email Notification of New Private Messages - Make sure it is not checked.
Show New Private Message Notification Pop-up - your choice
Be sure you "Save"
If all this fails then try removing your email address from your profile.
Disclaimer - I don't know nuthin bout no computers