It sounds like your starter motor shit the bed. It was spinning slower and slower as the motor died. Slim chance that it could be an intermittent ground at the starter since those contacts do corrode a lot. Look at where the hot wire from the battery connects to the starter. This will be the thick wire not the small signal wire. If it looks badly corroded disconnect the battery. Then disconnect the wire from the starter and clean up the contacts. Put it back together and see if it stars.
Sometimes rapping the starter's body, not the solenoid, with a hammer or tire iron, whatever you can get to it with, will cause it to start a few more times. If you want to try that. Have your kid turn the key as you rap on the starter. If it starts you have confirmed that the starter is the problem.
If when you turn the key you hear a click and nothing else happens. Then then you are hearing the solenoid engage and send power to the motor. If you don't hear a click or it clicks repeatedly it could be a bad solenoid or ground issue at the solenoid. If you want to eliminate the solenoid as a possibility. Turn the key to the run position. Then use a screwdriver to short across the solenoid to send power directly from the battery to the starter motor. If when you do that the starter spins and the car starts, then the solenoid is the problem. If the starter still doesn't spin then the starter is the problem.
If you look at the pic above. Terminal B is where the wire from the battery will be. Terminal M is where power leaves the solenoid and enters the starter. These are the 2 points you want to short across. It bypasses the solenoid and powers the starter directly. Just cross them for a moment. It will spark, don't be afraid.
You will know immediately if the starter turns. If the key is in the on position the car will start.
Sorry if this is over simplified but I have know idea what you do or don't know about cars.
I can't stress this part enough,
Be careful!! Make sure you are well clear of the fans, belts or any other parts that can rip your hand off if/when the car starts. Also, if the car starts, don't flinch and smack your forehead on the subframe. I've seen it happen. Hysterical as it is, it's not fun.
If you want to talk about it PM me for my phone number.
-Chad