You should download the 96 shop manual at seadoomanuals.net and look at the schematic for your ski. The manual will tell you if the gauges light up or the vts should work when the start button is pressed. If that works then it's a good sign the mpem is working.
If you think the start button and lanyard are working, then check the operation of the start solenoid. With the lanyard on and the start button pressed the mpem should supply a 12V signal and ground to the 2 small wires (yellow/red stripe and black) attached to the base of the solenoid which you can test for with a voltmeter. That should cause the solenoid to click and short the 2 large terminals on top together. If you see the 12V and ground control signals on the base but no 12V to the starter cable on the top, then replace the solenoid.
If you don't see the control signal on the base of the solenoid you need to retest the start button and lanyard switch. The schematic shows that each of those simply grounds a wire that goes to an mpem input which you can test for.