You have multiple possible problems. First, do you have a fully charged battery and is the neutral light on? The neutral switch turns on the neutral light and provides a path to ground for the starter solenoid through a diode. If any of the following conditions has occured: the battery is dead or very weak (less than 6 volts), the neutral switch is bad, the diode has failed, starter switch is bac, the clutch switch is bad, the solenoid is bad or the wiring between any of the listed components is shorted or broken, you may experience what you just described.
Start with the battery - make sure it is fully charged. Is the neutral light on or do any of the lights work? No lights - check the fuse. Lights on, clutch lever pulled in, starter button pushed in - does the solenoid click? No click, check the continuity of the clutch switch, then the starter button - if they are good, check the diode. If all is good, check that there is power on the yellow/red wire at the solenoid when the starter button is pushed. If that checks good, check for power on the yellow/green wire when the button is pushed. No power on the yellow/green wire - bad solenoid. Power on the yellow/green wire - no click - check for power on the green wire at the diode - no power - bad diode.
Finally, check the voltage at the battery with the engine running about 1/8 throttle. With a fully charged battery and the lights off you should see the voltage climb to about 14.8 volts then drop to about 13.2 volts. If it cycles within this range it tells you the charging system is working. If it doesn't climb, but drops slowly and steadily, it indicates a problem with the charging system and that's a whole 'nother chapter. With the minimum information given, I'm betting there's a problem with the charging system.
Hope this helps.
