I have found that the jet ski will start prior to entering the water, but as soon as I launch the ski will not start...unless I remove the air filter case cover.? Any idea why this can happen?

Your stator sounds like it maybe not supplying enough ignition spark when the motor is under a load. When you put the ski in the water the motor is under much more of a load then when out of the water or on a trailer. Those are the signs of a stator going bad. Another option would be leaking crank seals. The seals need to hold pressure to pump the fuel to the motor. Sometimes the crank seals can burn up the stator if the seals are leaking. You can remove the flywheel cover and to inspect for a leaky front crank seal. It should be dry inside, but if it is all oily and wet, your seals are leaking.