My bad on your other post. I did not pay attention to what you had written in full since it started out by saying no Internet access and I assumed you meant at all. If your Exchange server is local on the LAN, then you may try ports 25 for SMTP and 110 for POP (doubtful). It may require port 389 for Active Directory or the IMAP port (probably). Your Exchange admin can tell you what services/ports you need opened as they have some flexibility when they setup the server.
You can also try turning on the firewall, but leave all the default rules turned off (Allow). If it works, then turn one off and try again, and then again. If it doesn't work with all the default rules turned off, then you know it is one or many custom ports that need to be set. Again, your company Exchange and Network Admins will be the best resources here.