Occasionally, there are problems with the Outlook client but you really need to access a shared exchange mailbox. One way to do this is via the web:
http://outlook.com/owa/{emailbox}@vanderbilt.edu
So, if you are trying to access the Central Circulation email box, your URL would look like this:
http://outlook.com/owa/cencirc.library@vanderbilt.edu
It will then prompt you to log in, which you will use your own Vanderbilt email address and epassword and if you are authenticated & authorized, you will see the mailbox.