Try jumping the 2 LARGE studs on the starter solenoid.

IF it cranks, bad solenoid.

Clean all the connections on the battery cables. Also make sure the engine is bolted down snug to complete the ground circuit.

Take battery to auto parts store and get it load tested. They'll do it for free.

Just because it shows 12.6V, doesn't mean it has the capacity to crank the engine. 8 penlight batteries will produce 12V, but not nearly enough current.

I'm having the same problem with the same l120 John Deere I have replaced solenoid cleaned all connections all the way to where it grounds to the chassis. The Battery is a year old. It's got me clueless as well. My next thought was replace the starter to. It's obvious a problem with this model John Deere I have had more problems with this one then my last Deere.

The weirdest thing is if I let it set for a few minutes it will start right up then shut it off and all it will do is try to start the engine like it's not getting enough power. The battery shows 12+ volts. I used a meter to check power across the solenoid it 11.50 going in and almost 9.0 going to starter. My concern now is thet the new solenoid is bad to. I will do what you suggested though. Thanks.

Having same issue, new battery, new solenoid and new starter. When gets hot won't start. Cools down starts up.

There is a condenser in some JD. When that goes you get the symptoms you described