This sounds like an issue with that is called the transmission range sensor. This is responsible for telling the computer that the vehicle is in park or neutral and is okay to start the engine.
When the vehicle doesn't start in park but does in neutral then this is normally what it is. Unfortunately, the only way to test it is to monitor the sensor with a scan tool and see that it is telling the PCM the correct position. So if you don't have a scan tool we are going to have to get someone that does.
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Saturday, December 14th, 2019 AT 8:08 PM