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The code P0513 points towards an issue with the immobilizer. Here is some info for you regarding this code.
P0513 DODGE - Incorrect Immobilizer Key Read more: https://www.autocodes.com/p0513_dodge.html
The code P0113 points towards an issue with the input air temperature sensor. Here is some info regarding this code.
P0113 DODGE - Intake Air Temperature Sensor 1 Circuit High Read more: https://www.autocodes.com/p0113_dodge.html
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