Since my last reply, I have found the problem.
In the DMX_EntryPermissions table I found that there were many folders and files with PermissionID=Approval. With further investigation, many of the Approval tagged were associated with a RoleID=3 and RoleID no longer exists - RoleID=3 was delete from the Roles. And the critical piece is that EntryID=0 (The Root Directory) was tagged with Approval for RoleID=3. This could not be seen through the user interface because the Role was deleted. Also, I could not find in the User Interface how to change the permissions of the root directory.
To fix the problem, we cleaned out all entries in the EntryPermission table with RoleID=3 and cleared all the entries with PermissionID=4 (Approval). Now the files and folders are behaving as expected.
Thank you for your help.
Steve