Troubleshooting the Ignition System

First try a different spark plug. Hold the plug onto the head while kicking it over.
If no spark then make sure the screws holding the stator coil onto the cases are tight. They are the ground path for the circuit.
Next disconnect the CDI and put an AC voltmeter on to the wire from the stator coil and to chassis ground.
There should be around 400 ohms there if your meter is set to read resistance. If it reads infinite resistance then the stator coil is burned open. If it reads less than 250 ohms then the stator coil has a short in it.
Kick it over and see that you have at least 30 volts AC there.
Next connect the CDI but disconnect its output wires going to the high voltage coil. Hold them (touching the metal connectors) and kick the engine overly (slowly at first and then faster) to see if you get any little jolts of electricity. The output voltage is just a very quick duration spike which is why it is hard to read on a meter. If you get mini-jolted then the CDI is good.
If everything else is good then that leaves the high voltage coil and spark plug cap.
You can try screwing the cap farther onto the high voltage wire to make sure it is connecting good.
Make sure you can feel the spark plug snap into place into the spark plug cap when you are pushing the cap onto the plug.
Also visually inspect all the wires to make sure none have had their insulation rubbed off so that their copper wires short to chassis ground.
Also if the kill switch contacts are shorted closed (due to high current if the engine was killed while at high RPM) that would short out the voltage from the stator coil. It would also leave you thinking the stator coil is shorted out. Test it with an ohm-meter to make sure it works right. There should be infinite resistance till the button is pushed which causes very low resistance (which should be less than 3 ohms).