You have a couple of issues most likely due to neglect.
The START button is a ground signal to the solenoid (Yellow/Red wire on RH control). Locate where it comes from handlebars and test continuity to ground with a meter. Then go to the solenoid, repeat the test. And then ultimately, make sure the handlebar Y/R has continuity to the solenoid Y/R. You'll probably find a wiring issue along the way.
It could also very well be the button itself needs repair/maintenance. If the wiring deposit resolve it, open the control and inspect and repair anything inside.
Your coils: there's a BLK/WHT striped wire feeding power to the coils. Each coil has its own wire and the coils join together in a double female bullet connector. This is fed power through the KILL/RUN switch. Use your meter and confirm you have 12v at the connector. You also need to confirm the battery is fully charged and known good with voltage above 12.4v to start the bike.
A lack of spark at eh plug could be your points, condensers, or even the plug caps themselves.ey go bad after time, and each cap unscrews from the plug wire. Use yur meter and read the resistance of each cap (probe on either end). Ohms should be 5k, no higher than 7k Ohms.