won’t start, makes noise like a power drill that’s reached its torque limit and is spinning without trying to tighten further. Similar to timer install, but more rapid and not as loud, like a hand held drill. Seems to me the sound is from or near the starter. I’m thinking it is the starter rather than the battery, but could a low battery make the starter do that? Does the starter require a minimum power level before it will engage the engine?
Sounds like the solonoid isn’t advancing the pinion gear into the ring gear. Have your starter checked.
Check the battery, too.
The battery has failed, the starter solenoid will cycle rapidly when there isn’t enough power to operate the starter motor.