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If you pull off the red/blue wire at the solenoid will the starter disengage?
If you can go try that and let me know when you can please.
That wire is what engages it when the key is turned to start. If it stays engaged with the wire off, usually its because the solenoid is stuck on...i see that you have replaced it but i would try another one because i have gotten defective new ones before.
The starting circuit is real straight forward, the key puts power to the red/blue wire and it closes the connection inside the solenoid and lets power go thru the solenoid to the starter. It's either a defective solenoid OR the starter gears are too tight and the starter cant pull away from the flywheel so it stays engaged.
Sorry for the delay but mu computer locked up for awhile :-(
I have had 3 or 4 in a row that were bad right out of the box before so it sure wouldnt surprise me.
The solenoid is a simple thing. It gets power on the side with the battery cable and when the red/blue wire gets power from the ignition switch, it swings power over to the other stud with the cable that goes to the starter.....very basic system.