Troubleshooting the Ignition System
Testing for spark:
Remove the spark plug and connect it to the spark plug cap. Manually hold the spark plug with cloth onto the cylinder head (metal to metal) and make sure the side electrode is sideways so you can see the spark gap clearly. Kick over the engine to see if any spark is generated. It is hard to see in full daylight so it's best to do at night or inside. If no spark happens then there is a problem. If you have spark but the engine won't start then one of these problems exist:
1. Compression is being lost due to loose head nuts or leaking head gasket.
2. Something is really wrong with the carburetor such as a pilot jet being clogged or an intake air leak (possibly at the crank seals).
3. The ignition system is too weak for the engines compression ratio. Ignition magnetos normally weaken over decades and then won't create enough voltage when kicking over the engine.
If the engine has a high compression ratio it requires a very strong ignition system (for high spark voltage). If the ignition is weak then it can spark in free air but not in the compressed air inside the engine. You can try lessening the spark gap so a spark can happen with the low spark voltage.
Test the Stator Coil:
Use an AC voltmeter to test for 25-50 volts coming out of the stator coil as you kick the engine over with the spark plug removed. First disconnect the stator coil wires from the CDI. I prefer using an analog voltmeter such as this one: [voltmeter] If the voltage is there then the stator coil is OK. But some stator coils provide ground to the CDI by its clean metal-to-metal connection to the cases. Good metal to metal contact there is essential. A loose or rusty connection there creates resistance which lessens spark strength.
Test the CDI:
You can test for total circuit performance (without determining the peak output voltage which requires a special test circuit or a meter that can read peak voltage) by just holding the CDI output wires while kicking over the engine. Someone may have to help you with that. Start out very slow and gradually kick faster till you feel a minor shock. I prefer this basic method because the output voltage lasts for only a few thousandths of a second which most meters can't register. If you are getting shocked then suspect the high voltage coil or the spark plug cap or the spark plug as bad.
You can't test for resistance at the input or output of the CDI because the input is a combo of resistance and a diode, and the output is capacitance and a diode.
What normally goes bad in a CDI is one of the diodes, the SCR (black transistor with 3 legs), and the large output capacitor (the largest component on the board). Unfortunately the circuit components are buried in epoxy and impossible to get to.