Start the ski, and put a volt meter across the battery terminals. Rev the engine to 5000 rpm's and make sure the voltage is between 13.5 and 14.5v.
If it's high or low... it's the regulator.
It could be the stator... but it's very un-common for them to go bad. You can check them out though. Just check for an open between the output wires, or a ground from the wire to the engine case.
It could be the battery... but if it starts the ski, then it should be OK.