iPhone 5 - digitizer busted?

My iPhone 5 is less than a year old, it is still covered by the regular warranty, i do not have apple care. I dropped my phone from a height of about 3-4 ft, and the screen loss all sensitivity. The screen itself is intact,however on the inside of the prhone some vertical lines are now visible. I have been told something called the digitizer is busted. Will apple replace this phone for me, or fix it? I am aware that more than likely i would have to pay for this service, but i was wondering how much, if they would be willing to do anything at all.

thanks