when i ask who is your host, i mean what company are you using for web site hosting space.
the smtp server:
smtpauth.earthlink.net
looks like it would require authentication. The email passwrod server behavior does not support passing a user name and password to the SMTP server to authenticate, it cannot be used with SMTP servers that require authentication.
your host should have an alternative SMTP server that can be used that does not require authentication, you should contact them to find out what smtp server to use with a php script sending email.