Kyle,
I just did a couple of quick diagnostics, and it looks like the SMTP server on your - what looks like - Exchange server isn't working.
The MX record is in the DNS and I can telnet to the POP3 port (110) without any problem. However when I try to telnet to the SMTP port, where the mail server receives the e-mail from other servers, it does not respond.
The above symptoms would allow your mail client to connect to the server and authenticate, but there wouldn't be any mail. Messages sent to accounts on the server may not bounce because the MX record is present in DNS and the SMTP server didn't respond with a rejection of the address. As a result the sending server may keep trying to send the message for - depending on how it is configured - several days. You my get a notification after a few hours that the receiving server was unreachable and the sending server will continue trying.
It has been a while since I worked with the Exchange server. The last version I used was 5.5, so I don't know how relevant this would be, but I recall that they had "agents" for each messaging protocol: one for POP3, one for IMAP4, and one for SMTP.
By default, the SMTP server agent needed to be turned on before it would receive any mail from the Internet. If it wasn't only users within the same domain (eg. @discoweb.org) would be able to e-mail each other.
Hope this helps.
Victor