OK, it's definitely a permissions issue, but let me ask:
First, are the Private Pages under the 'web' context in the tree (if not, what context)?
Second,
Go to Security -> Access Controls (User Groups tab)
Right-click on the user group for the front-end users
Select Update User Group
Click on the Context Access tab
List the context, the minimum role, and the policy for each entry you see there.
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PLEASE, PLEASE specify the version of MODX you are using . . . PLEASE!
MODx info for everyone:
http://bobsguides.com/modx.html