They usually carry two pumps one for the rear circuit and another passes the front suppliers, and are operated independently.
Do not specify through which tubes put air, if it was by the tube or by the water outlet suppliers. Anyway, if you put pressure air, some tube may have been released and the water does not go to the suppliers.
With the standing engine and the contact placed, it acts the water pump control, if you make noise the pump works correctly. Look to see if you have released a tube, or clean the wardrobators with a fine wire in case they are still stuck.
Another way that I use to clean the suppliers is to disconnect the plastic tube that comes from the pump (to prevent it from being released on the pump side) and putting water in reverse direction with a plastic syringe. "Loose the tube, water loads the syringe, you support it on the supplier and squeeze it to inject the water in the opposite direction and drag the shit that is obstructing it." Luck.