The Department shall not authorize payment under Section 5 or accept guardianship for any child for whom a final dependency order has been entered prior to January 1, 1964, under the provisions of the “Family Court Act” or for a child accepted for care or placement by a private child care facility prior to that date, except for a child who has been receiving public aid under Articles IV, V, VI, or VII of “The Illinois Public Aid Code” who is no longer eligible for such aid but who continues to be in need of foster care.