That Relay is a starter circuit relay. It is open any time you dont have it in neutral to prevent you from starting it in gear. Do you have a Volt meter? A test light might work. On the starter solenoid unplug the red connector and check the voltage at the pin that the white wire hooks to by touching the positive lead of the voltmeter to it and the negative lead to the battery negative post. It should be the same as battery voltage.
I attached a little homemade drawing of what to do with your meter.
I would say so. If the fuse is good and both the positive wire from the battery to the Starter solenoid is good and the negative wire from the battery to the side of the engine is good and is grounded good on the engine I would say the solenoid got damaged. You could take a jumper wire and jump from the white wire pin in the red starter solenoid plug and touch it to the battery positive post and see if the anything powers up like the lights or the neutral light with the key turned on.
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