If all users on you BES are able to receive and send mail and PIM sync is working ok, its unlikely that something is wrong in AD, must be special for th besadmin user.
If you have a mixed environment of Exchange 2007 and 2003, the besadmin mailbox should be on the 2007 server (and, it must have a real mailbox).
restart the domain controller(s), restart the Exchange server, restart the BES server.
If this does not help, you could try to change the besadmin account to a new one, and see, if this makes a difference:
KB04293-How to Switch BlackBerry Enterprise Server Service Accounts