If you move to a new Exchange Org in the process you will have to start from scratch with BES. The same DB cannot be used between Exchange Orgs, it cannot and will not work. Best bet is to uninstall the old BES, install it on the new hardware and activate your users again, you'll have to reactivate them anyways. Might as well start with a fresh BES.
When starting over you will have to make sure the new server has all the pre-reqs in place, go to
BlackBerry Technical Solution Center and look for the install guide for the version you are installing. Also, set permissions for your BESAdmin account:
View Document
That doc will show you all the permissions needed. Then it's just a matter of installing the BES and activating the users. Not much to it really.