WisdomRacer,
Here is a good explanation on why you need the CDI in the circuit.
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Something to try :
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Unfortunately without having the proper specs for testing each electrical component for the proper resistance, voltage, and continuity it becomes a remove and replace kind of situation. Could get expensive.
Some people had issues with the remote start/kill systems that come installed on the the kids ATV's that produce the no spark issue.
One more thought is if the quad has clutch/brake lever safety measures installed on the unit you may need to apply the lever (pull in) for the quad to start.