Hi and thanks for using 2CarPros.
It sounds like you have two different problems. Not starting in neutral is related to the neutral safety switch. Take notice if the back up lights are working properly because the neutral safety switch and back up light switch are one in the same.
As far as the running issues, my first suspect is a faulty crankshaft positions sensor. This sensor is responsible for ignition spark and when the begin to fail, the symptoms you described are very similar. Interestingly, the crank sensor is operated by engine speed. Therefore, if the engine fails to start or stalls, it may not set a trouble code.
Take a look through his link:
https://www.2carpros.com/articles/symptoms-of-a-bad-crankshaft-sensor
Now, if you have a live data scanner, plug it in and go to engine RPM's. If you find the RPM signal drops and then the engine dies, replace the sensor.
Here is a link that shows in general how one is replaced. It will help guide you.
https://www.2carpros.com/articles/crankshaft-angle-sensor-replacement
Here are the directions specific to your vehicle for replacement. The attached pictures correlate with these directions.
PROCEDURES
REMOVAL
Picture 1 indicates location
Fig.12 CKP Removal/Installation - 5.7L V-8
See Picture 2
The Crankshaft Position (CKP) sensor is located at the right-rear side of the engine cylinder block. It is positioned and bolted into a machined hole in the engine block.
1. Raise vehicle.
2. Disconnect CKP electrical connector at sensor.
3. Remove CKP mounting bolt.
4. Carefully twist sensor from cylinder block.
5. Remove sensor from vehicle.
6. Check condition of sensor O-ring.
INSTALLATION
1. Clean out machined hole in engine block.
2. Apply a small amount of engine oil to sensor O-ring.
3. Install sensor into engine block with a slight rocking and twisting action.
CAUTION: Before tightening sensor mounting bolt, be sure sensor is completely flush to cylinder block. If sensor is not flush, damage to sensor mounting tang may result.
4. Install mounting bolt and tighten to 28 Nm (21 ft. lbs.) torque.
5. Connect electrical connector to sensor.
6. Lower vehicle.
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Let me know if this helps or if you have other questions.
Take care,
Joe
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Thursday, January 24th, 2019 AT 7:05 PM