try these steps
1) try to ping the mail.domain.com from remote location and see if you can ping, if you can not ping you have connection or dns problem
2) if you can ping try to connect to the server using telnet and see if you can connect to the server
if you can not connect make sure your smtp server (exim ) is running on the server.
3) now you need to login to the server using ssh and see if the exim is running and listening to the port 25
one way to see
Code:
netstat -nap | grep exim
4) if you get out something like
Code:
cp 0 0 0.0.0.0:465 0.0.0.0:* LISTEN 26597/exim
tcp 0 0 0.0.0.0:25 0.0.0.0:* LISTEN 26592/exim
which means exim is running and listening to the port 25 and 465
if you can connect and if the exim is running, please make sure your client ips is not blocked by firewall, if you are using linux and iptables you can do
Code:
iptables -nL | grep client_ip
5) if the ip does not get blocked by firewall, try to see what kind of error does the client has on the exim_mainlog file , you can check
Code:
exigrep emailaddress /var/log/exim_mainlog
that should give you more info,
hope that helps, if not seek professional admin help