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You have a short to power at some point. When you say the starter shorted, can you explain what happened? Also, have you checked to see if the starter relay is fried? Try this, remove the starter relay and see if the starter engages when you connect that battery. At least that will help narrow down possible wiring issues.
If you look at the pics below, pic 1 shows the starter relay location. It is number 12 in the pic and I circled it (under hood). Remove that and see what happens. If the starter doesn't engage, switch that relay with one that is known good. Don't put the possibly bad one in any other place. First, see if the starter engages with a different relay. Here is a link that explains how to test a relay if you want to check it:
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit
Here are a few links that explain how to use basic testing equipment when checking the relay:
https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
https://www.2carpros.com/articles/how-to-use-a-voltmeter
https://www.2carpros.com/articles/how-to-check-wiring
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Pictures 2 and 3 are of the starting system. In picture 2, I high lighted the wires from the ignition switch so you could see how power travels to the starter. It is only a partial picture. In picture 3, you see the relay and then a purple wire going to the starter. That is the smaller wire on the starter. That specific wire should only get power when the key is in the start position and no other time. In this case, it is getting it all the time; thus, the starter wants to stay engaged. By removing the relay and checking it, we first determine if the relay is bad. Also, it will tell me if the problem is before or after the relay. For example, with the relay removed the starter still engaged. To me, that indicates there is a short to power at some point either where the relay plugs in or that purple wire is shorted to power. Are you certain that the main wire between the battery and starter (the larger one) and the purple wire (smaller one) are not crossing at any point and both are clearly separated at the starter? Make sure of that because I've seen it happen before where they are actually touching.
Take a look at the schematics I attached and I'm sorry for the sad looking arrow I drew. Still not too good at drawing on a computer. LOL
Let me know what you find.
Joe
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Sunday, June 16th, 2019 AT 9:38 PM