Hate to say it but besides being broke, its hard to fix. Nothing is accessible without removing the lower crankcase.
The only problem I've ever heard of is that the shaft iteself breaks and the starter goes limp. Enough of the shaft stays in place between bearings, that the oil pump gear remains perfectly fine.
I guess you could have broken a tooth and jammed it in.
If a tooth broke and jammed wouldn't it freeze everything. The bike runs fine.
I've got to think about it a little, but there is a springloaded pawl mechanism that resides within a gear. When you press down on the kicker that engages the internal flange of the gear, turns the gear which turns the mainshaft I think. When the engine catches, the mainshaft turns the kickgear which disengages the pawls and lets everything spin. The kick gear is spinning the whole time, so it couldn't be a tooth, you're right. It must be in the pawl mechanism, that is, the pawls have broken or stopped working.
Never seen that happen before, its a pretty stout mechanism. Nevertheless, you're looking at an engine removal and teardown, at least the bottom end.
PS: I still don't think thats it. I'll have to look, I've got one apart.
PPS: Just looked at a fishy. Not much else it could be, but I can't see it.