Yes you can. You can setup your new Google account to download your emails from the CatholicWeb server by following the instructions at http://www.catholicweb.com/googleoverview/old_email.cfm.
It appears your e-mail was not migrated to the new server. Go to the home page of CatholicWeb.com and read the e-mail conversion info for more details. You need to reply with your full name, catholicweb.com e-mail address, your password, your phone number...
If you are having problems retrieving your old e-mail on the old server, double check you are going to http://mail.catholicweb.org:8383 (note the .org). Logon with your username, but use catholicweb.org (i.e. yourname@catholicweb.org) Enter your old passw...