There are different reasons why your POP3/IMAP server could be down. As a first step can you check if your MTA is listening on the ports 143 / 110 & 995 ?
e.g.
root@intranet:~# netstat -na |grep 110
tcp 0 0 0.0.0.0:110 0.0.0.0
LISTEN
tcp 0 0 0.0.0.0:8110 0.0.0.0
LISTEN
root@intranet:~# netstat -na |grep 143
tcp 0 0 0.0.0.0:143 0.0.0.0
LISTEN
root@intranet:~# netstat -na |grep 995
tcp 0 0 0.0.0.0:995 0.0.0.0
LISTEN
If one or all of the above is not listenining then that's where your problem is on the setup of postfix & listening ports.
again so your mail log should be another place to check.while you are trying to check the mails on LAN or WAN, Login as a sudoer or root and check the maillog see example below.
root@intranet:~# tail -f /var/log/mail.log
Check for obvious error messages.
Below is a sample successful mail log from one of the servers i manage.
Sep 23 21:50:23 intranet dovecot: pop3-login: Login: user=<shepherd@botsnet.bw>, method=PLAIN, rip=168.167.182.62, lip=10.0.0.254, TLS
Sep 23 21:50:23 intranet dovecot: POP3(shepherd@botsnet.bw): Disconnected: Logged out top=0/0, retr=0/0, del=0/4, size=9041
If you have iptables firewall please enable the ports used by your mail server. I would recommend ports 25 / 587 / 143 / 110 & 995
should you want assistance send me a mail at shepherd AT botsnet.bw or shepherdzw AT gmail.com
