Well, it's not the battery, not solenoid, not the ground strap...now for the bad news...the internal gear (made of nylon) that the planet gears engage from the starter motor. Not a great design as far as I'm concerened as it is the weak link and where all the torque is developed to engage the ring gear.
Well, the good news is this is the only occurrence of this I know of, on here.
Which means your the lucky one. Congratulations.