There is no way to check the electronic ignition modules with an ohm meter. The old coils that worked with Points you could, but not the electronic ones.
Make sure you are getting a good ground on the sparkplug and look real close for the spark. Many have a very slight ark, turn the lights off in your shop to see it if you have to. As much as you would love to get the neighbor kid to hold the sparkplug wire while you crank it, please refrane from doing it. Some of those modules put out 28kV. They will make that poor unexpecting neighbor kid scream and piss down his leg.
Next remove the starter assy and find the ignition module. There should be the high tension lead (spark plug wire) and since you mentioned the saw had a lot of polymer there should be two other wires coming out of the module. Unplug the other two wires and then recheck for spark.
If you have spark, that means that the wires have grounded themselves out some where on their journey to the switch. One wire is a Ground wire. The other wire has the electrical Juice running through it.
Good luck