If it is less than or close to a year you may want to consider taking the phone to an Apple Store. It would probably cost less and save time, if the phone is damaged it would give you more options. I only say this because I had a phone die and was due to the circuit board, apple swapped it out for me.
If you are determined to figure this out, try plugging the phone into a computer to see if the computer recognizes the device. It could be possible the digitizer died.
If not, open the phone and check for loose cables, could be possible a cable came loose and crossed a wire. The battery could of also have been shorted out.