The most likely item that will cause this problem is a defective solenoid as all power to the starter motor is transferred through a copper disc at the rear of the solenoid. a test that you can perform on the solenoid which is the small cylinder on top of the starter has two large terminals at 12 o'clock and 6 o'clock and two smaller terminals a 3 and 9 o'clock. When you turn the key to the start there is a 12 volt signal that goes to the small terminal at the 9 o'clock position ( I'm 90% sure that it is this terminal) which energizes the solenoid and passes the power from the terminal at 12 to the terminial at 6 o'clock which is attached to a conducter that goes into the startermotor at the rear of the starter. The disc inside of the solenoid will get corosion on it and can hang in the activated position therefore allowing the starter to continue to run until the key is turned to the off position. Thesolenoid can be replaced seperately and should cost around $20 and is very easy to replace versus about $80 for a starter which is also fairly easy to replace also. Hope this helps.
The color of the wire you are looking for in #1 is purple. If in the process of doing the checks, you find any loose bolts, You might want to tighten them and retest. There is a return spring between the solenoid and the plunger that goes in the middle of it. That spring could have been left out if there were repairs to the starter recently. I have never seen that spring break though. Good luck.