'No support yet' ... a day later from original posting. Sigh! This is community support ... no one paid to support. So please be patient.
EMail issues are or could be quite involved. So I'll at least begin the 'discussion/cussion':
In your Moodle setup, are you using an SMTP server to relay mail? or are you using the built in Moodle PHPMailer?
Do you have access to the SMTP server logs?
Do you have access to your Moodle servers logs? (not the logs inside Moodle, but operating system logs)
Are you running Windows, Linux, Mac?
on shared hosting dedicated hosting or ???
Moodle isn't and never has been a mail server. It's just an app which might have need of sending mail ... notifications, forum postings, new user, forgot password, etc.. Thus, it actually might be trying to send in all those thing, but network it's hosted upon doesn't allow port 25 (smtp) mail traffic out OR the receiving mail servers are blocking any mail from your Moodle server because of spam checking.
'spirit of sharing', Ken