I'm not sure how the key works w/ your ski. I know some older ones don't have a coded key like the newer one but have more of just a kill switch. But saying that your key is working properly I would check to make sure you are getting voltage to the starter solenoid when you push the start button. If you don't you know your problem is between the battery and the solenoid and if you do then it is probably either the solenoid or your starter.