Thousands of needy Illinoisans are going without medical care due to unlawful delays by the state, a new court filing claims.Lawyers for a class of low-income people have argued that state agencies responsible for Medicaid are violating an order that requires them to extend benefits to people whose applications for the program are still pending.The motion, filed this week in Chicago, claims the state’s Human Services and Healthcare and Family Services Departments are months late processing applications, haven’t …