Is there water in the ski? in the rear electric box? Sounds like no maintenance.
To figure out what's wrong, unplug the black/red wire between the coil and mpem (part with fuses) and see what happens. If it has spark then the mpem probably has an issue. If no spark, either the stator or coil are to blame. Also if it starts like that use the choke to kill since the kill switches will be bypassed.
Ensure that you have the correct spark plug and the gap is the correct gap, and torqued. Consult your manual, to be sure.
Change out Coil. The orginal signal to spark the coil is generated at the stator. The exciter coil on the stator must be good to generate spark. Also, the start stop button and lanyard post must be good to allow the ignition to work. If any one of those things is bad, you would see no spark.
I have seen spark plug wires burned at mid point and hard to detect its failure, and change them before I buy a coil, as there is no test for them, they Work or Don't Work.
A free floating piece of metal inside the mag housing can short out the system regularily, or irrregularly, depending on what it touches. If it is not a broken gear tooth or starter shaft spline, it could be a piece of the centrifical weight holder retainers inside the bendix, as they break off regularly and there are 6 of them. They are U shaped and about 1/4 inch long x 1/4 inch wide. Not only a huge hazard to the destruction of the stators coils, but also a hazard to the ignition pickup by gounding it out killing spark and the power to everything else.