Admin and Office Secretary type users have access to all cases by default.  All other types of users need to be assigned to cases.  "Grant Access To All Cases" button under the Staff tab may be used to assign a non-admin user to all old cases.  However, when a new case is added, the new case is not automatically assigned to non-admin users.  Check the box "Automatically Assign To New Cases" to assign a new case to a user when the new case is added to your account.  If this box is not checked, a newly added case will need to be manually assigned to the non-admin user using either "Grant Access to All Cases" button or by checking the box under Grant Access/Rates tab of the case.