Ok so outgoing mail isn't working at all? (sorry I missunderstood when you said someone hadn't recieved any emails, I thought they were on your network
One this to verify is wether or not the SMTP server actually sees you and your domain as valid. Are you comfortable using telnet?
We can verify domain and connectivity locally (and remotely) using telnet on 25 to test. What do you show for output regarding the following:
Substitute your.mail.server for your mail server and when you do the helo command ... just use your domain. I used the same account to send as I did recieve to test and make sure they are both valid accounts in your domain and on your mail server.
# telnet your.mail.server 25
Connected to your.mail.server (some.ip.address).
Escape character is '^]'.
220 your.mail.server ESMTP Postfix
mail from: firstname.lastname@example.org
rcpt to: email@example.com
354 End data with .
this is a sample
250 Ok: queued as C958E20C4CF
Connection closed by foreign host.
What do you get for errors?