Post model number from under seat, thanks.
CRAFTSMAN Tractor Parts | Model 917276410 | SearsPartsDirect
Results engine information
"Hands on", check all linkages & hardware, springs, etc. making sure everything is secure & not worn out.
http://www.husqvarna.com/ddoc/husi/husi2007_aaaa/husi2007_aaaa__5040542-05.pdf
First a question, does it shift when the unit is not running? If it does, the first thing I would check is the drive belt and drive tension pulley. They are not releasing and allowing the drive pulley on the tranny to keep turning. Second, is check the brake, making sure it is stopping the drive to allow you to shift. If the unit will not shift with the engine not running, I'm afraid that you will have to pull the tranny and replace the shift keys. This is not a job for an inexperienced mechanic or homeowner.
Being able to shift with the unit off tells me that the tranny is not the problem. Try this to help pinpoint the problem. First with the unit off, put it in any gear and set the parking brake. Now check the drive belt tension, the belt should be very loose. If it is still tight you may have it routed improperly. If you don't have your owners manual, you can download a manual at Sears Parts Direct. Page 24-25 show the belt routing. If the belt is loose you may have to adjust the brake on the tranny.
Have to ask, what did you do to the unit before this problem showed up?
While you are sitting on the unit, engine not running, have your son watch the belt action while you operate the clutch petal. When you push the clutch petal down, the belt should be extremely loose. As you let up on the pedal the belt should slowly start to tighten up. If all looks correct, jack or block up the rear end, put the unit in neutral and try turning the rear wheels together in the same direction. The wheel should turn easily. If they do, shift to first gear and try again. If both wheels turn together, repeat in each gear. If the wheels turn in all gears, I suspect the tranny is OK, but either you have a belt routing problem, or the brake is not stopping the tranny gears, to allow shifting.