I checked with my host and everything is correct
Obviously not, else it would be working.

the test emails are not there, it appears that they are not leaving zc
You made the mistake of hosting with GoDaddy, and around 6-8 weeks or so ago they changed their mail system to only allow SMTP Authorised emails to be sent out, disallowing the standard Sendmail protocol.

Your SMTP settings in Zen Cart will need to include the User Name for the email address plus the password.

Vger