Here is some more information. I had a bad MX record in my DNS. Now things look better. I can now send and recieve from inside the Main Library building using an e-mail client such as Outlook (on the same network as the ISPConfig server)
From Outside the building I can recieve e-mails, and I can send to e-mails with the cass.lib.mi.us domain. I still cannot send to anyone other than cass.lib.mi.us e-mail accounts from outside the Main Library.
I suspect that this is some sort of relay setting problem. Can anyone advise me where I can check the relay settings, and what they should be set for in order for me to be able to send to non cass e-mails?