Does the fan spin when you twirl it with your finger or a stick? engine cold and ignition off for safety. If it does not spin, the fan is defective.
When you find the sensor, disconnect it and short the wires with some conductor (a piece of wire)
If it runs, the sensor or wiring is faulty. If it does not run, the fan may pe the problem.
A complicated fix may be a blown head gasket of a failed engine.
Bypassing the dealer may be a poor choice.
Any decent mechanic should be able to find the fault - does one service your car now?
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