Re: ignition
First, do you have the correct switch (as in one for a two stroke). It should have two "M" terminals on it. Next, are you certain the neutral start switch in the control box is functioning properly. It should allow the engine to start in neutral but kill the starter in forward and reverse.
Since the starter does not energize, the "S" terminal on the switch is the place to start. When the key is in the START position, check for +12 volts on the "S" terminal. If it is present, then the problem lies between the switch and solenoid and it could be a corroded connection in the large engine harness plug at the engine.
If you do not see +12V at the "S" terminal then check for +12 volts on the "B" (battery +) terminal. If you have +12V there, but not on the "S" terminal in START, you have a bad switch (highly unlikely). If you do not have +12V at the "B" terminal, +12 volts is not getting from the battery to the solenoid, up the harness to the switch. Again, blown engine fuse, bad battery cables or connections, or bad wiring between the engine and console.
A simple check of the starter and battery is to use a jumper cable. Connect one end to the battery POS terminal and touch the other end to the large terminal on the starter. If the starter spins it is good. If not, attach the second jumper cable from the NEG battery terminal to the engine block and repeat the starter test. If it now spins you have bad cable connections. So attack this logically -- isolate parts of the system.