Code P0339, crankshaft position sensor replacement

P0339 indicates a problem in the crank position circuit, not necessarily a bad sensor. It could be a broken wire or bad sensor or a fault in the ECU that reads the crank sensor.
First thing to do is look at the tach while cranking the engine, is the tach at least bouncing while it turns over? If no, then it's likely a bad wire that is taking the crank signal down. It generates an AC waveform that the PCM uses to read speed and crank position. Testing it isn't really hard. You use a meter to verify the sensor has continuity. Then you go to the PCM and find the Brown wire on pin 40 and the white wire on pin 55 both in the C1 connector. Then you check there for the same resistance you saw at the sensor's connection pins. If the wiring is good, it should show continuity. If it does, then it could be a failed PCM. However, I would use a scope to check the signal first then the cam signal as well. If it's a broken wire you simply replace the wire. It could be a bad connection as well. So, a good visual inspection first.