Tom is probably correct and here is a way to confirm where the problem may be
Assuming the engine turns freely.
I like to start from the starter motor and go backwards .
Do the following 5 tests, regardless of the results from an or all of them as there can be more than one problem and you want to isolate where the problem lies.
Elimination of individual parts is important so you know by the end, the battery, solenoid & heavy power circuits are all in good order.
1) try to jump the starter motor directly from your car or truck.
+ on the starter first then - to a good ground near the starter ( drain plug of lift hook are good )
Starter turns = starter good
2) do the same directly from the mowers battery
Starter turns = mower battery good
No turn = duff battery, recharge it & try again.
3) leave ground jumper in place ( from step 2 ) & try key start.
Starter turns = power connection good but ground connection suspect ( most common )
Confirm it by trying again, extra ground removed
4) Remove the trigger ( thin ) wire / wires from the solenoid.
Ground one on a 4 wire solenoid & bridge from the hot terminal to the other.
Starter cranks = solenoid good.
Solenoid is not polarity sensitive, BUT THE WIRING IS so make sure you remove the thin control wires.
Note a thinner wire on the hot terminal is not a control wire. It is the main power feed to the mower.
