Hello,
The only thing I can think of is the wiring is messed up somehow or the PCM needs to be replaced. Lets check the power wires first to make sure nothing is crossed.
Here is a guide to help you see if there is power coming from the ignition switch when it is not suppose to:
https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
If there is not power and the starter engages it is a PCM problem and it needs to be replaced.
Below is the starter wiring diagrams and PCM location which you will need a shop to program for you.
Check out the diagrams (below).
Please let us know what you find. We are interested to see what it is.
Cheers, Ken
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Tuesday, January 23rd, 2018 AT 11:10 AM