I don't know how you could have multiple computers connected via a switch and dsl modem. Perhaps you have a router/firewall there.
dsl modem has router functionality->
fritzbox 7140
What do you see when you log onto the server as root, and type:
telnet smtp.orange.nl 25
[root@woody ~]# telnet smtp.orange.nl 25
Trying 193.252.23.135...
telnet: connect to address 193.252.23.135: No route to host
How about:
telnet smtp1.google.com 25
[root@woody ~]# telnet smtp1.google.com 25
Trying 216.239.57.25...
telnet: connect to address 216.239.57.25: No route to host
[root@woody ~]#