This has been very frustrating, if you search for GoDaddy and PHPMailer you'll find loads of posts about how PHPMailer needs to be configured in order to work with GoDaddy's hosting.
I tried using some of the configuration information I found online but I wasn’t having any luck. I kept getting “Error: The following From address failed:” despite trying several different addresses (including valid addresses that I had setup on GoDaddy’s cPanel)
I finally came across Aravind is Online blog which nudged me in the right direction (http://aravindisonline.blogspot.co.uk/2012/01/phpmailer-with-godaddy-smtp-email.html)
You cannot use an external host to relay email messages. You must use the following host: relay-hosting.secureserver.net
I setup a mail user specifically for PHPMailer (I am hosting a subdomain so all my email services are elsewhere)
Use PORT 25 (numerous guides suggest 465)
Set SMTP Auth to true, Aravind’s guide suggests to set this to false, however this didn’t work for me.