Which SMTP server are you using? I'm migrating a php site to GoDaddy and email is driving me up the wall. The original host allowed one to send email via smtp.office365.com. Out of the box, GoDaddy does not allow this. I think they might if they also host your email for you but for my client, their email is hosted on Office 365.
I had to change the code to use GoDaddy's SMTP server plus I also had to create a dummy email account with the required username & password for authentication to work.