I have a John Deere 125 lawn tractor. Tried to start it up recently and would not turn over. In fact, no sound at all when turning the ignition key. Same thing happened to me last year and it turned out I needed a new battery so I bought another new battery and still the engine will not turn over. However, the lights work. Also, when I jump the solenoid the engine turns over. Using a multi-meter I connected the ground to the battery negatvie post and touched the solenoid connector that leads to the ignition with the positive end. No voltage showing. With the multi-meter black wire still touching the battery negative post I used the red wire to touch the bottom post of the solenoid that leads to the starter. Again, no voltage showing. Should I assume from the results of these two tests that the solenoid is not functioning and needs replacement?

You should get voltage to the small connector from the ignition switch when its turned to crank. All the solenoid is, is a switch that allows you to control a large current... with a small current. If you jumped that small connection to the battery and it cranks... you have a wiring or a switch issue.

Check your pto lever or switch .
Check fuse by battery.Luck