My guess is that it is either the start button itself, the wiring that goes to and from it, or the solenoid is not working anymore. I would start at the solenoid, if you have power at the low current feed wire (the small one) on the solenoid when you push the start button, the solenoid is your problem. If not, I would start at the battery and trace back toward the solenoid and see where you lose power, that will be where you find the problem.
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Yours truly, sincerelly, love always, Josh aka The DirtDemon.