I created a new role that will have access to the Incident table. After configuring the ACLs for Incident, the new role still does not have access.
Out of box, ServiceNow provides a Business Rule named 'incident query' on the Incident table that will limit the query results for users who do not have the ITIL role or higher. This BR is set to run before the table is queried in order to apply the conditions. To learn more about Business Rules, refer to the documentation in the Additional Information section.
De-activate or edit the Business Rule so that it fits your business needs.