If the axle is spinning inside the rim then the key is missing. Make sure you check both sides. If one side is missing it will do the same thing. Check both sides as well as make sure the free wheel lever is pushed all the way in in the rear of the tractor. With the brake unlocked and the free wheeling lever at the rear pushed in try and push the tractor. If the tractor rolls then the key is missing in one of the rear wheels. This is a good way to test.
Hello, my name is Kevin.
I don't have a whole lot to add to Jcooks answer as it sounds like the correct approach for your situation. I can however provide you with a break down of the transmission so that you can see where the bearings and keys all go.
Hope this helps,