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Next, check the state of the contacts in the bottom of the kettle itself and in the base it sits on. These can sometimes get distorted or eroded by sparking or oxidised by water, with the result that the contacts in the bottom of the kettle no longer make contact with the ones in the base. This may be puzzling at first since continuity tests on both the base and the kettle show no fault in either, yet the kettle doesn't work. You may be able to effect a fix by cleaning or bending the contacts back into shape. The ones in the base are deeply recessed for safety reasons and you will have to remove the bottom of the base to gain access.