An end user with only snc_external role is receiving a "404" page not found error when trying to displayed a non public service portal page.
However, the page has the scn_external role under the Roles field.

If a Service Portal page is not public, users with the snc_external role won't be able to see it. So the role need to be added in the Roles field of the page. But if User Criteria is configured, the Roles field is not displayed. 

It User Criteria is configured, then the Can View and Cannot View TABs (Related Lists) will be displayed in the page and the Roles fields will not be displayed. So the options to include roles for the pages are:

OPTION 1.
1. Go to Service Portal >> Properties
2. Type snc_external under "List of roles (comma-separated) that bypass User Criteria validation in Service Portal."

OPTION 2.
Under the "Can View" tab, add the snc_external role or group that contains the snc_external role.