How to ensure that the digitizer is faulty?
Open your settings menu and go all the way to the bottom, open Developer Options.

In the Input section, find the options called Pointer Location, and check it.

This is a feature for developers that shows the raw data from the digitizer.

Move your fingers around on the screen, and watch what you see, if your finger seems to disappear from the screen, Android is not seeing any data about it, it is a problem with your digitizer.