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I agree with Bulbous, you problem is more likely a faulty fan resistor then a switch problem.
In the photo you can see the black fan motor (LHS of photo) it mounts into the white plastic, just to the right of the fan motor you can see the brown plug for the fan resistor.
You will also need to remove the interior fan and check that it spins freely by hand as this could be that reason the resistor has burnt out.