I’m not too good with Exchange. However I would first of all make sure the outlook profile is set up correctly and that the user can communicate with the exchange server and send/receive e-mails okay. and the the exchange server recognizes the user profile/account.
As far as the address book goes, I think you would want to try and get the personal.pst file or outlook.pst file from the “broken” computer and import it or insert the file on the “new computer”. Otherwise you might have to manually rebuild an address book.
Again I’m not too good with Outlook so take that for what it is worth.
Happy New Year.