From another site...
GoDaddy does not let you send emails via external SMTP on a shared hosting plan.
Here's GoDaddy's own words:
We appreciate your feedback and apologize for any inconvenience, however, due to security reasons, we are not able to allow the use of external SMTP servers in a shared hosting environment. If you need additional SMTP relays, you would need to consider a virtual dedicated or dedicated server.
So.. I guess the short answer is, you need a better host.