If it was the stator you would have water in the oil, the stator is wet with oil on the 84 200ES Big Red and i highly doubt thats it.
I would bet on electrical, check the connections in the boot on the left side down by the sub trans. Also pull the plug on the CDI and check that out. A little water proofing goes a long way on the CDI.
As for the electric start, the starter relay, the interlock relay, and the push button are the likely suspects but check the starter motor actually works. You can take jumper cables or a jump box and put the negative to the frame and touch the positive to the cable connection on the starter. If it spins over then you need to chase through the wiring. The starter relay are a pretty common failure but the start button is the one i always seem to fix on the 200's.. Pull out the screw in the bottom of the handlebar control and take the button off, make sure both wires are connected in there and clean up the switch, a lot of the time the one wire breaks off and needs to be resoldered.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....