my cooling fan is on full speed
That tells us that the "engine control relay" output from the RCM (Relay Control Module) is not there. This means the ECU does not power up, but the Fan Module does power up, so the fan module runs the fan at full speed cuase the ECU is not telling it what to do.
This is almost always bad solder junctions on the RCM or a bad engine control relay on the RCM.
The Crank sensor has nothing to do with engaging the starter.