The SMTP server is clearly saying that it won't send mail because you're not authenticated. This is a standard requirement, virtually all email servers accessible from the internet require authentication.

It can be tricky to get this right, your service provider should provide info, ok their documentation looks awful. I suggest:

Server type: SMTP
Username: Either your-username or your-username@mail.orcon.net.nz try both. Replace your-username with your username.
Port: 587
Secure connection: TLS or None try both
Server: mail.orcon.net.nz
Secure authentication: Plain password.

So there are 4 combinations to try (2 username x 2 secure connection).

If it still doesn't work then try deleting the account and creating a new one.

If that still doesn't work try creating a test gmail account and trying to send with that.