If it's agitating and draining at the same time, it's probably the control board. I see a lot of GE washers with gunk in the pressure tube. You would think this would cause flooding but it usually doesn't. The gunk allows pressure to build up in the tube and then acts like a check valve keeps the pressure in the tube. The symptom is dry agitation.
Try disconnecting the pressure tube at the switch and see what happens.