If you can get the ski/mpem to "recognize" the key, by the motor turning over, using the start/stop button, then the mpem is good.
Try, removing the sparkplug boots, clipping the wires a 1/4in off, then apply the boots back on. They screw onto the wires.
You can also see if the coil is getting any type of signal, by using a "light tester" at the white wire, while motor is cranking. If it lights up, then the stator and mpem is good, and your problem then lyes with the coil or the wires, and or the ground leads.
If it doesnt light up, then remove the front cover of the motor, and inspect the "pick-up" coil, thatsa mounted on the inside, behind the plate. The bracket is notorious for breaking.