If its just the start button that's easy to take apart and clean, just pull out the bottom screw and remove the start button from the bottom of the left handlebar control. Then try jumpering the wires in that and see if it cranks, if it does its probably just a dirty start switch, i take them apart and clean them with a brass brush, a little de-oxit spray, and then some dielectric grease and put it back.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....