Starter/flywheel noise when moving

You could possibly have a bad park neutral safety switch , power ( voltage ) from ignition goes thru the park neutral safety switch to the S terminal on the starter solenoid . Does your vehicle have automatic or manual transmission ? And you should have voltage drop testing on the starter circuit done . Starter Voltage Drop You could have a bad battery cable .

Check the distributor

It is not the reason, but if the clutch does not fully disengage from the Flywheel, extra drag could occur.

If you can still drive the car, have a starter draw test performed with the transmission in neutral. The draw test can show the health of the starter. For that matter, use the Emergency brake and start the car in neutral anyway, although you may need to press the clutch to engage the starter. See if there is less noise by starting in neutral.

Probably a starter. It sounds like the starter solenoid is working, but the starter motor is not energizing.

You could try this simple trick, but Im about 85% sure you have a bad starter.

Have a buddy help you push the vehicle in neutral for a short distance. When you get it moving at a walking pace, put the transmission in Drive, and let the vehicle come to a stop. You may hear a little clicking, but thats OK, it wont hurt anything. Put the transmission back in Park and try to start the engine again. Sometimes the starter gear gets stuck on the flywheel and it wont engage when you try to start the engine. This trick may move the flywheel a little so the starter can engage.

It could be either the flywheel or the starter.
If it's grinding, don't try it again until you've removed and examined the starter and flywheel. If the starter solenoid isn't fully engaging the bendix, it will cause the gear to grind; replace or rebuild the starter if that's the case.
But you should examine the flywheel to see if it is seriously damaged from the problems you've had. Put a mark on the flywheel using a magic marker, then examine the flywheel as you slowly turn the engine by hand. (make certain that the ignition is off when you do that, you don't want anything bad to happen to your hand.) The mark on the flywheel will indicate when you've been able to examine the all of the teeth on the starter ring.

It could be the starter, is it high pitch screeching, metal against metal, sound? Or more of whine? If it's metal against metal, the teeth on the flywheel ring gear might be damaged. If it's a high whine you are probably hearing the electric motor part of the stater and the "starter drive" is bad. The stater drive is part of the starter, it's the gear that engages with the flywheel gear. It is a one way clutch, it is supposed to hold when the starter is turning the engine. But, freewheel when the engine starts so it doesn't over rev the starter motor. When the drive goes bad it freewheels both ways. If you think the flywheel teeth are damaged you could try turning the engine by hand a little, WITH THE KEY OFF! Sometimes you can put a wrench on the alternator pulley nut and turn the engine a little. This will move the damaged teeth away from the starter and it might work now. Good luck.

Broken flywheel teeth will give you an unmistakable noise when starting. Either the starter drive is getting stuck or putting it in neutral is allowing you to start it because the neutral safety switch is either out of adjustment or bad. (I'd bet on the switch)

YOU CAN REMOVE THE SERPENTINE BELT AND START THE ENGINE BRIEFLY TO SEE IF NOISE IS STILL THERE. IF NOISE IS NOT PRESENT CHECK ALL BELT DRIVEN COMPONENTS FOR LOOSE BEARINGS OR EXCESSIVE MOVEMENT. IF NOISE IS STILL THERE THEN PULL DUST SHIELD UNDER VEHICLE AT FRONT OF TRANSMISSION. THIS WILL ALLOW YOU VISIBLE ACCESS TO THE STARTER DRIVE(THE PART THAT MOVES OUT TO ENGAGE THE FLYWHEEL ON BACK OF ENGINE)WITH AN ASSISTANTS HELP START THE VEHICLE(WEAR SAFETY GLASSES)AND WATCH AND LISTEN. IF THE NOISE IS IN AREA OF FLYWHEEL YOU WILL SEE THE STARTER DRIVE(IT HAS TEETH ON IT)STAYING ENGAGED TO THE FLYWHEEL, IF THIS HAPPENS YOU CAN TRY SHIMMING THE STARTER BUT MOST LIKELY THE STARTER WILL NEED TO BE REPLACED DUE TO A BAD STARTER DRIVE(OR BENDIX) RETURN SPRING. HOPE THIS INFORMATION HELPS!!

You are moving the strater away from the flywheel when you put shims on it, this normally will make it worse. A clang will tel you its too close. When you got your starter shims did it come with a little piece of wire about the size in diamiter of a ink pen refill? if so that is the gauge for using the shims.You place it on the shaft of the starter, and it should just slide between the flywheel and the shaft. You may need to move the starter closer to the flywheel, this can be accomplished by only shiming the outside bolt on the starter- hope this helps.

that sounds correct what happens is the starter still tries to engage the flywheel and grinds the teeth off both. Replace switch then worry about starter flywheel if it starts fine don't worry about it you may have saved it if you didn't let it run that way long