After searching I have found the schematic for the one I have which is about 20 years old. Reading these things is always a challenge and quite frankly even though I studied it before it was like the first time I ever looked at it. The one I have does show a magneto going to a coil for the spark plug. It doesn't look like points and condenser or module are used to produce the AC needed to transform low voltage to high voltage. Or at least the schematic didn't show them. I don't know if any magneto uses them or if they produce a wave or broken form of electric. All I know is you can't transform DC volts it must be converted to something like a wave form.
With this additional info I still cannot say what is wrong with the original posters problem. If it would be the same as mine I would still consider the control board but with so many models there can be many other factors too that I never had experience or could imagine.