5252 differential problem

[Cub5k]

I have a 2004 5252 2 wheel drive with about 650 hours. Never a problem until I lost drive in the left wheel while pushing snow. The tractor freewheels unless the diff lock is engaged. When the diff lock is engaged everything works fine except that it is only driving the right wheel. PTO and loader work fine. Looking at the parts diagram for the trans I would say that it either broke the left axle or spun the splines off the end. Replacing axles is a fairly simple process but I don't know if I need to open the transmission to check for metal particles etc. Any advice?