The stator is the device that produces a voltage to the coil in order for the spark plug to spark. It is located under the flywheel which is behind the left side engine cover (next to the shift lever). You have to pull off the flywheel to get to the stator, which requires a flywheel puller. On our '88, the stator had a coil that produced energy for slow RPM's and another one for high RPM's. You can go to www.buyakawasaki.com and see a parts diagram for your bike. However, after thinking more about this, I'm not sure the bike would even start if the low speed coil was bad. A service manual could tell you the procedure for testing the stator or a competent shop could test it for you. We bought a used one from a bike junkyard for $75.00. There are also companies that rebuild them (they are listed in the back of most bike magazines). Based on all that you've done, and the fact that it just started out of the blue, I still think it's electrical, even if it's not the stator.