A soft or hard reset may fix this problem if it is software related.
To do a soft reset:
If the display is off, press the POWER button to turn it back on.
If you've set up a lock screen, you need to unlock it.
Press and hold the POWER button, and then tap Restart.
When asked to confirm, tap Restart.
If it does not respond when you touch the screen or press the buttons, you can still restart it. Press and hold the POWER and VOLUME UP buttons for at least 10 seconds. It should now restart.
Be sure to back up any data and files you want to keep before you do a factory reset.
To do a hard/factory reset:
Press and hold the VOLUME DOWN button, and then press and hold the POWER button.
Wait for the screen with the three Android images to appear, and then release the POWER and VOLUME DOWN buttons.
Press VOLUME DOWN to select FACTORY RESET, and then press the POWER button.
Your phone should be set back to factory setting now.
If resetting doesn't get your touch screen responsive then you might have a faulty digitizer or a loose or broken digitizer ribbon cable or connector on the motherboard. The digitizer part of the screen is responsible for sensing touch. If you find fault in the cable you will need to replace the digitizer.