:welcome:
Follow the thick red lead on the started down to where it bolts on to something.
That is the solenoid.
Bridge the two thick wires on the top one or both might have a rubber boot on them.
Use an old open ender, it will flash quite strongly so be ready for it and make sure you do not touch anything else with the spannar.
If the engine spins freely then the solenoid or the wiring to it are bad.
Naturally clean all of the connections first and the ground wire from the battery to the mower. both ends before you pronounce the solenoid deceased and replace it.