I was able to send an email through GoDaddy using these settings in the web.config:
and this code:
var SmtpClient = new SmtpClient();
SmtpClient.Send("emailaccount@yourdomain.com", "to@whatever.com", "subject", "body");
Note I believe that the from address in the email you are sending has to be from your domain. I tried sending an email as coming form another domain and got an error message.
You have to make sure you have an email account in GoDaddy, you can check by logging in and going to Products > Email > Email Plans. You also have to make sure SMTP relay is turned on, it was turned on by default for me. Also important to know by default my GoDaddy account only allows me to send 250 emails a day.