I had this happen to me on my F-935. One of the drive axles broke and the only way to move it was to lock the two axles together with the differential (axle) lock.
What you need to do is lift the mower one side at a time and while the differential lock is depressed try to rotate a tire. The engine does not need to be running for this by the way. If you can rotate a tire then that is the side you need to work on. It could also be that one of the drive keys is broken where the axle goes into the brake drum. You'll need to take the wheel and brake drum off to have a look.
Edited to add that if you aren't sure what you are doing then it might be a good idea to take this machine to a mechanic.
If you search for an " John Deere F-935 service manual pdf " you should be able to find a service manual online which would help if you need to replace parts. If you need to see what a component looks like internally then John Deere has a pretty good parts website that you can print parts diagrams off of.
