Hello my name is Dave.
Do I understand correctly that it starts and actually runs when you jump it off (at the relay? If this is correct the first thing I would recommend is to try putting it in neutral and see if it will engage the starter then. If that doesn't do it then I would test the relay. Here is a link to our tutorial on testing the relay:
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit
If is not actually starting but the engine is turning over the first thing to check is if the security light stays on with the key in it, if it does then the key and the ecu aren't communicating usually to a bad key or the ecu isn't properly programmed to the key.
Please keep us up to date on your progress and thank you for using 2CarPros!
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Monday, April 6th, 2020 AT 4:21 AM