Small Engines (Lawn Mowers, etc.): Axle falls out..., axle shaft, shocks

Question
I recently got new tires and messed up when removing the wheels on my JD Stx38 yellow deck.  I got the wheel half way off and didn't know what to do so i beat the axle shaft with a hammer and rod until the wheel came off.  Anyway, new tires are great but I must have broken something in the transmission because the axle slides out and will not engage.  Is this fixable?  if so could i do it myself?  And is so what do I need to look for whaen the transmission is apart?   Or would it be better to purchase a used/new transmission?  I have done some small engine work, brakes, starters, shocks, plugs and such on cars but haven't worked with transmissions before.   Thanks for your help.

Answer
Doug
I am a little confused here you say you removed the wheel on the deck? That has nothing to do with the transmission. I also need to know the Model # of the mower JDSTX38 is the deck # The transmission is what you are talking about I think please clarify.