Crankshaft sensor code PO339

You have checked the ground, but what about the lead? I would look for (1) continuity through the wire, end to end, and (2) a short by looking for continuity between the lead and the negative battery post (any continuity there indicates a shorted wire).

What about continuity from end to end of the lead wire?

I am trying to dig it up but not seeing it yet. But I would personally bet that your problem is in the connector or within a couple of inches of it. Hook your leads up, one end on the connector, and the other lead several inches up the line. Then jiggle it around and I will bet the continuity comes and goes. Replace the connector.

Just to jump in here. When you have your scan tool connected, when you crank the engine do you see an rpm signal? If you do not then you will need a lab scope so you can graph the sensor.

You should also remove the sensor and have and assistant turn the engine over by hand and inspect the carrier plate for damage. Also using a pry bar, check for play on the crank shaft by putting light up and down force at the harmonic balancer and push in and out on it to make sure there is no play.

Last you will need to have the cam and crank locking tool to lock the cams and crank in place so you can verify that the timing belt is installed correctly. If all that is good, and you have a good wave form, inspect the connections at the ECM.

The lock for the ECM at the air cleaner is very delicate and breaks/jumps easily. Make sure connections are properly secured and lock and that no pins are damage. If all is good I strongly recommend you buy the bracket and sensor from the dealer. If okay and harness is good then the ECM is bad and that requires programming.