If you have a VOM- voltage-ohm meter- and can get to the back of the switch, simply check continuity between the two "M" terminals. They should be open, with infinite resistance when in the run position and closed with no resistance in the stop position. If not, the switch is bad and should be replaced. You can stop the engine by jumping white to blue on the engine terminal or if the colors are different, "STOP" to ground.
If the choke solenoid is not working and the start position on the switch is also not working, there is an excellent chance that the switch is bad. Check there functions to see id there is 12 volts at the switch terminals when the key is pushed (choke, "C" terminal and turned to start "S" terminal.