Hello,
If the mail() function exists and php isn't throwing an error, then the problem is with the exim setup. If a domain has been added to the server, in no case will mail be able to leave the server as long as the domain is in the /etc/virtual/domains file, *even if the MX records point elsewhere*. I've added a feature in 1.20.6 that allows users to remove their domain from that file by going to the the MX records screen and setting it to not use the local mailsystem.
John