Depends how it got cracked, or more precisely how you convince them it got cracked.
If you broke the screen by accident then yes you pay for the repair, if it broke due to a manufacturing fault they pay.
Though unless it's less then a couple of weeks old you won't convince anyone it was a fault on the screen.
and quite expensive, but nobody is going to be able to give you a price from the information you've given, does your laptop have a 7inch screen or a 21inch screen, there would be a huge difference in price between them!