Small Engine Troubleshooting Problems? Ask a Mechanic Now.
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When the starter does not engage do you hear any clicking or noise?
You may have a bad cell in your battery. Do you have a way to either load test the battery yourself or get it in to someone that can? You will need to load test it not just check volts. It could show that it is good with a voltage check but when you load it the voltage may be dropping too low to function.
I have seen batteries have a bad cell or strap between the cells that you allow them to work sometimes and not others. I just needed to verify first that we didn't have a battery problem.
You had stated earlier that playing with the shift lever had normally fixed the problem in the past. You may want to focus on the safety switch that is there, the machine has to be in neutral before it can crank over if this safety switch is acting up then it could be your problem. If there are two wires coming to this switch you can easily unplug the wires from the switch and jumper them to see what happens, if the engine cranks then you know that the neutral safety switch is bad.