I posted this a while ago
"I have a 3.0L V6 2000 Ranger XLT Extended Cab. It's done me good. One day, my starter died in my work parking lot. We have free parking, so I got it fixed when I could. Ran and started up fine for about 8 days until I tried starting it up at my house to go to work. The starter would not stop turning the engine over. It kept going until it was burnt out. From that, I've put in two new starters w/ solenoids, replaced the ignition switch, rewired the starter and solenoid a dozen times, and replaced a blown 50A starter and ignition switch fuse/relay. I can't think of anything else that could be a problem. What can I do, other than get a new vehicle, which is not an option for at least 2-3 months?"
I forgot to mention that my problem is that the truck does not start. It does not turn the engine over at all, now. I turn the key and the starter makes a noise, but it must be the solenoid because the starter motor is not turning. People have told me it's a bad ground, but which one in particular should I look for? I took off the connector for the engine block ground wire, cleaned the dust and crap off, and put it back on. Still nothing but that slight buzzing or whirring. It's done this with 2 new starters. I also did the headlight ground, just because it was something to do. If needed, I will take a video of the noise and the truck and post to this thread. Thank you very much

 

Starter motor needs full battery voltage to turn engine
If it continued to run/turn with key NOT in the START position then it was still getting Full Battery voltage, so thats the pathway you need to look at

Pathway is this

50amp fuse(engine fuse box)---------Ignition switch----7.5amp fuse(in cab panel)--------------(Neutral switch)-----------Starter Relay(in engine fuse box)---------(Computer Ground, PATS)

50amp fuse(same one as above)---------Starter Rely------Starter solenoid(on starter motor)

Battery positive-------starter solenoid------starter motor-------Ground

So...when you turn the key to START, 12volts is sent from 50amp fuse thru the 7.5amp fuse to the Starter Relay, IF computer has Grounded that relay(PATS test OK) then Starter Relay will "click" closed.

Starter relay closing sends 50amp fuse power to Starter Solenoid on the starter motor
Starter solenoid moves starter gear out to engage flywheel and sends Battery Power to starter motor.


I have skipped over the Neutral switch because you don't say if you have a manual or automatic transmission, they use different systems.

But basically the Neutral switch prevents the 12volts from ignition switch from getting to the starter Relay unless Clutch Pedal is pushed down to the Floor, or unless automatic is in Park or Neutral
Each one of these switches has 12volt power when key is on, not just when key is in START, so a short at this type of switch could cause starter to continue to run, but key OFF should have stopped it.

My best guess is that you got a bad starter solenoid on replacement starter motor, these can fuse closed because of the 100AMPS they pass to starter motor, if that happens then starter will just keep turning until battery is disconnected or runs out of power.

This would also heat up positive and negative battery cables so they may not work well again and would most likely ruin the battery, or at least shorten its life by quite a bit.

So your current issue could be starter relay, battery cables or battery itself
A 12volt car/truck battery will show 12.3volts or higher if it is good
12.2volts and below is a failing or bad battery

PDF is wiring diagram for your system