Asuming you have a backup copy of the Exchange 2003 ‘MDBDATA’ folder, you can extract the mailboxes to PST files using 3rd party software as described below
http://social.technet.microsoft.com/Forums/en-US/exchangesvradmin/thread/49aaa2ae-fe6d-4d15-87a5-43714b31547f/

The manual way is to setup a exact installation of the Server 2003 Small Business Server for example in a virtual enviroment.
All the parameters like computer/domain-name/updates-servicepacks and ip-address must be the same.
Then stop all exchange services and move the old database folder (MDBDATA) to a temporary location.
Move your backup-copy of the MDBDATA to that folder and restart the services.

It could be that the database has a status:  “Dirty shutdown” (%exchange%\bin\eseutil.exe /mh priv1.edb)
the repair can also be done with eseutil (%exchange%\bin\eseutil.exe /p priv1.edb)