John Deere 1050 - Question about electrical

John Deere 1050. Battery deceased over winter. Purchases new battery. Installed, tractor immediately started. Ran for a minutes than parked it. Two days later, tractor started immediately, drove it to where tree was down, loaded wood into bucket, needed to get off tractor to open gate, and moved gas lever too far down into off rather than low and turned the tractor off. After getting down from tractor, something else came up, and a day/half later returned to move wood to woodshed. I guess I didn't turn off the key when the tractor stopped running. Tractor would not start - assumed dead battery, and charged the battery. Still would not start. Neighbor checked battery and it was charged. There is spark at starter, but beyond starter cannot find electric. Fuses all appear OK. Took off switch but cannot find electricity to switch. This tractor is now an albatross. Last year it overheated and blew off the radiator cap. That was repaired and then I was told it needed thermostat and then it needed a pump. . . and then it needed. .........and the final bill after one thing and then another ended up costing more than the tractor is worth. Please tell me something simple and inexpensive to check on this tractor!! Also, the PTO is not engaged and spins freely by hand. TIA!

Check your battery, starter, and ground connections. Take them apart and clean them so they are shiny. Put them back together and make sure they are tight.

On the electrical clean and check all the connections and test the battery to make sure it is good first.
On the PTO sounds normal to me that you can spin it without it engaged.

Not sure if this will help. I always hot wire at the starter to determine if the ignition wire is not
causing the solenoid not to engage. You can cross it over at the solenoid as well. Worse comes
to worse you can start direct on the starter and see if it works Make sure in neutral