From the figures you are quoting, it looks very much as if the thermostat (sensor) is faulty. 4K ohms is what could be expected when the 'stat has opened and broken the circuit. The 27 ohms across the element terminals implies your heater is between 1.5 and 2kW. If you bypass the thermostat, does the heater work? DON'T leave it switched on with no thermostat though!