I had a kitten once that got hurt, didnt know how. Found him curled up in his basket , purring, but he wouldnt come out.
While we all know purring can mean contentment, I found (from the vet) that it can also occur if the cat is in shock. So if your kitten is laying there purring now, don't assume he is happy.
Look at his gums. If they are white, he is in shock, and needs treatment asap. They should be pink, normally.
When I took my kitten to the vet, they gave me a weeks worth of liquid pain meds, which helped a bit. Unfortunately, when the meds were done, kitty was in great pain again, crying, growling, etc. We had to put her down. :(
Try to keep your kitten still, try to get her to drink fluids. I don't think there is too much else you can do at home. Implore your parents to do what is right for this kitten. Best of luck!