Hi,
Was the starter replaced or only the solenoid? Also, I attached a pic below of the starting system wiring schematic. I circled a fuse to check and the relay that was mentioned by Heyman. He is certainly correct that a weak relay could cause the issue.
Now, if the entire starter was replaced, we need to confirm two things. First, make sure the battery power (larger wire on the starter) isn't being interrupted. Check that using a volt meter or multi meter. Have a helper crank the engine and see if voltage is lost.
Next, the smaller wire on the solenoid which is yellow with a light blue tracer should receive 12v only when the key is in the start position. Have a helper turn the key to start while you check to see if power is there.
Here is a link that explains how to check the starter:
https://www.2carpros.com/articles/starter-not-working-repair
Also, make sure the battery terminals are tight and clean and the main ground from the battery which attaches to the engine block is tight and clean at the engine. If you move wires around near the battery and it makes a difference, check for corrosion to the wiring resulting from the battery acid.
Let us know what you find. Also, if you could record what is happening so we could hear and see it, it may help us. And one last thing, see if the vehicle will start with the shifter in neutral as well as letting us know if it has a factory installed security system.
Let us know.
Joe
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Monday, February 22nd, 2021 AT 8:37 AM