The most likely problem is a loose connection on the inside.
Check the connections of the ribbons on the inside of the device. Follow the [guide|25453|motherboard removal guide] to get to the ribbons.
If this doesn't work, the digitizer may need to be replaced. However, a guide is currently not available for that. To replace the digitizer, one would follow steps similar to the [guide|25455|screen replacement guide], but put the components in a new digitizer.