Here is the checklist I use to quickly diagnose a no-crank situation. In your particular case, please repeat step #2 at least ten times, just turn the key and watch the light or meter. The reason is I want to test the ignition switch contacts and by turning the key ten times you should either see the light/meter respond every time or if it does not then your switch is suspect.
Start with the basics, don't overlook anything and verify all components.
First, check the fuse(s) and check battery voltage - above 12.5 volts should be good.
Second, check for power at the small terminal of the solenoid while depressing the clutch/brake pedal and holding the key in the start position (you may need an assistant to sit in the seat to override the safety switch). If your solenoid is a four wire solenoid, check both small wire terminals as one is ground and the other is power from the ignition switch. If your solenoid is a three wire solenoid, make sure the solenoid body is not corroded where it bolts to the chassis of the mower as this is your ground path back to the battery. If in doubt, remove the solenoid and clean the mounting area down to bare metal. If there is no power to the small terminal then your problem is most likely a safety switch, ignition switch or in the wiring.
Third, check for power from the battery to one of the large terminals on the solenoid. One of the wires is connected directly to the battery and has power all the time so one of the large terminals should light a test light or show 12 volts on a meter.
Fourth, check for power on the other large terminal of the solenoid while holding the key in the start position (you may need an assistant to sit in the seat to override the safety switch).
Fifth, check for power at the starter while holding the key in the start position (assistant again).
Sixth, check your ground circuit back to the battery.
Please perform the above checks and report back with your findings in the order listed. Be as specific as possible with voltage readings as this will help diagnose your problem quicker. If you don稚 know how to perform the above checks, just ask and I will try to guide you through it. Youtube also has some videos and as you know a picture is worth a thousand words.
Your answers to the above checks will determine where we go.