Lots of hamsters do not run wheels they hate them so no probs on that .
The suspected injury thing , and not using the wheel.
I suspect it has hurt itself in or on the wheel and that why it stays clear of it , possible broken toes or bones from a wheel or a badly dislocate hip or joint..
If it is more than a month ago that it stopped being active then the break / injury will have healed and you have a lame hamster.. if it is eating and drinking OK then it is managing and it could live to 18 months to 3 years old.
Leave the toys in the cage as hamsters like to rub up against things they have scent marked and sometimes they just like to lay in them rather than play with them.
Check the rear end of the hamster, is it dry beneath its tail or has it got wet tail. (a dark wet area and it smells evil , not that clean musty smell you normally find)
Like I have said on prevoius posts I farmed hamsters and other small mammals by the thousands for 16years. So my advice is if it has got wet tail have it put down humanely ..nothing cures wet tail in a hamster over about 4 months old.
If it has wet tail from shock of cold / draughts , handling , injury or disease it will have gone too far by the time you see and smell it...its kidneys are starting to fail and it will be in pain.
Hamsters are naturally incontinient and wet tail is the result of an illness injury or infection that makes it worse.
A vet might sell you some antibiotics to try and add to its water for a cure it but they rarely work. I had a couple of vets who used telephone to ask me for help etc in diagnosing and helping out WRT small rodents at their surgery .
Should you have your worst scenario ....before you get another hamster wash out everyting in hot soapy water , rinse it off , disolve any urine scale with lemon juice over a couple of sessions , use a bit of wood to rub it in and start breaking it up , don't use a sharp implement , when its all off re wash the cages and all gear , rinse and then spray them with a solution of baby bottle sterilizer ( correctly diluted MILTON ) leave it on for an hour or so then rinse off and let it dry over night before getting that furry replacement.
regards
David