Starter not engageing flywheel?

[Gunner]

I think a starter would engage even with a wrong tooth count - it might engage irregularly, or make horrid noises, or even break some flywheel teeth, but a count or two off wouldn't entirely prevent engagement.

A "faint spinning noise" sounds like a starter that's not engaging anything at all. I'd guess wrong starter, faulty starter, or not enough current to throw the pinion forward.