Here is a snapshot of the Yamaha Parts Fiche. The Starter Clutch (8) inside bore slips over the Hub of the big idler gear (6) that spins freely on the crankshaft. The outside ring of the Starter Clutch (8) is bolted onto the back side of the flywheel (not shown) and is carried onto that gear hub as the flywheel is installed. The starter clutch locks the flywheel to the idler gear (6) when the idler gear is spun by the starter motor. The flywheel is oriented by a key that slips into that rectangular slot on the crankshaft (on the left, not numbered) and is taper fit locked onto that shaft such that it cannot spin on the crankshaft.
Are you talking about the woodruff key (half moon shaped) having fallen out when you tried to put it back together? It orients the flywheel with respect to the crankshaft. and might have come out or broken after that single initial start. If the flywheel is not properly seated with the key in its proper place, by torqueing the nut that brings it all together to the proper torque value, It can spin on the crankshaft and the engine will not turn over when the starter motor is spinning.
Also, the outer rim of the starter clutch needs to be bolted onto the back side of the flywheel for the engine to turn over with the starter motor, just in case you did not do that. The bolts (9) are drawn pointed the wrong direction in the picture below, if I am not mistaken.