This paper introduces a novel cable-driven robotic platform to assist with and train head-neck movements. Poor postural control of the head-neck can be a debilitating symptom of neurological disorders like amyotrophic lateral sclerosis and cerebral palsy. Current treatments using static neck collars are inadequate and there is a need to develop new devices to empower movements and facilitate physical rehabilitation of the head-neck. Existing exoskeletons using rigid linkages are limited by their restrictive structure. By contrast, the cable-driven robot presented in this paper does not constrain motion and allows for wide-range, six degrees-of-freedom control of the head-neck. We present the mechatronic design and control implementations of this robot, as well as a user study to demonstrate its feasibility to assist with head-neck motion and apply a resistive moment on the head using a target reaching task. Our results show that neck muscle activation increased by 19% when moving the head against a resistive force field and decreased by 28-43% when assisted by the robot in two different assistive control modes. Overall, these results provide a scientific justification for future design and control optimizations to enable movement and studies to identify personalized rehabilitation for motor training.