OK, process of elimination: (assuming a good, fully charged battery installed properly, good connections, grounds, etc......)
1) Press Start button, no DESS key inserted yet....do guages wake up? If yes, then you have power to the SS button. If NO, then you have an electric pathway issue...check the electric pathway front to back, EVERY piece of wire from connector to connector.....corrosion is insidious and just a little will cause you FITS
2) If the ski wakes up on the Start button push.....INSERT DESS key.....BEEP BEEP? If yes, the key is recognized...that's good. If NO, the buzzer is probably dead (common issue)....replace the buzzer.
3) If the ski wakes up and the DESS key is inserted and the SS button is pushed and the ski turns over trying to start.....(this tells us the buzzer is dead for sure, the solenoid is working (you might hear the click which is the electromagnet pushing a bar inside the solenoid to short the solenoid posts together to send the battery power directly to the starter motor), the starter is probably OK (if the engine is cranking over).....you can take out the spark plugs while doing this to take the compressive load off the starter which should allow the engine to spin over easier). If all that happens....we are getting closer.
4) Are you getting spark at the plug ends.....remove plugs and put back into the boots and see if spark is jumping the gap at the plugs.....
5) Have you tried squirting a little pre-mix directly into the spark holes, putting the plugs and wires back in and cranking her over? If she fires even briefly.....you MOST likely have a fuel delivery issue and it would be time to service the carb(s)......
