I have a John Deere L110 lawn tractor and it won't turn over.New battery.When I turn the key nothing happens.

Two quick thoughts: try jumpering the solenoid and also check every safety switch.

I would check for power to the solenoid while cranking, can use a test light or 12 volt bulb, a second person can help.
And I believe the negative to the solenoid is through the safetys,(seat, neutral?)etc.
Need to determine which, then you may need to test at ignition switch, depending on the results of the above test.