I believe this may be due to php mail from posts I have seen on the forum, I have used the php page listed to test the php mail and that said it was ok.
When the PHP mail() test script says 'Ok' it means the server seemed to have accepted the message for sending. Final delivery of the message, on the other hand, is left up to the server mail software. Are you able to send test messages to a remote test address not on your server?
In ListMail with bounce enabled your return path is your 'Bounce to address'. With bounce disabled your return path is the 'Administrator Email'. These should usually be set to an address on the same domain of ListMail and may (rarely) need to be existing accounts or forwarders on your domain.
You may want to try enabling the following line in config.php to enable a 5th paramater to PHP mail(), forcing the 'Return-path':
$phpmailf = 1;
Please let me know if I can be of further assistance.
Regards