GoDaddy has a specific server and port you may need to use if you are sending email from a server inside their network. If your website is hosted by them and you are sending email from an Asp.Net script (such as PDshop), you will need to use the SMTP server below.

This is what you use with PDshop:
relay-hosting.secureserver.net

The port is the standard port 25, do not enable SSL as it is not supported.

UPDATE 8/18/16:
Some GoDaddy users have reported problems with email sending.  While the email appears to send, it never arrives when using the Relay SMTP server or there are significant delays or in cases it ends up marked as Spam.  We now recommend using the Email SMTP Server settings as shown in your GoDaddy Email Setup Center.

We recommend these settings as an example:

SMTP: smtpout.secureserver.net
Port: 80
Do not enable SSL
Enable SMTP Authentication and enter your email and password.

The reason we recommend using Port 80, and not enabling the SSL, is to reduce the chance of connectivity issues.  Often times the server or network firewalls block connections on ports 25 and 465, whereas Port 80 is usually open.  

For additional assistance with SSL/TLS secure ports, contact our Technical Support for help with configuration.