There are diffrent types, in fully electronic versions the cars ecu provides a signal, pwm but not the same pwm the motor is driven with, but a reference signal, the fan controller uses this to generate the actual pwm that goes to the motor.
The fact yours is low and high speed suggest that it similar to a peugeot system where there is a transistor or relay switch and a power resistor which drops the voltage in low speed, the latter is the one that usually fails, the resistor burns out.
I would see if you can power the fan directly at full speed, if it runs full speed then its either a duff switch unit or possibly the wiring has broken, being burnt by the exhaust is common, or worn through on something moving.
I cant see your schem.