There are two small wires coming off the starter relay (solenoid). On is orange, one is black.
1. Make sure black is grounded.
2. Energize the other, orange wire with 12 V. Easiest way is to touch it to the big red cable coming from the battery. This should activate the solenoid and turn over the engine. If it doesn't, then the relay is bad. Replace it.
3. Assuming 2. was successful, the problem is in your start/stop switch.
4. Plug in the lanyard, unplug the harness from the ebox - both plugs.
4. Ohm between the red/orange wires going to the start/stop switch and push the start button. You should see an open circuit (infinite ohms) when the button is not pressed. You should see a short circuit (very close to zero ohms) with the button pressed.
5. If 4. was successful, the problem is in the harness connections to the ebox. Check the connectors for corrosion, check the short wires between relay and harness.
6. If 4. was not successful, remove the switch and start finding out where it's busted. Might be the internals of the switch. Might be the harness up to the switch.
7. If you cannot find anything wrong with the wiring, open up the switch and clean it. The contacts are made of copper and corrode easily.