OK, Now that the problem is solved (hopefully), I'll share my solution:
No PHP code changes involved here!
Go to the email configuration page in the ADMIN system.
I was only able to get SMTP method to work.
I had to use the mail relay server "relay-hosting.secureserver.net" provided by godaddy as the smtp host. This may be different for your machine - contact godaddy to confirm the name of the Mail Relay Server for your configuration.
You must set the email to be sent from a known domain to YES. This forces the emails to use the SENT FROM address you will set up next.
You must use an email address like
[email protected] (though not required to be an actual mailbox) in the SENT FROM option.

VERY IMPORTANT==> The email address must contain your domain in the address.