This is a common problem with the iPhone 5C, it is caused by the digitizer connector on the logic board. It is a connector that has no metal clips at the ends causing it to be a weak connector. if you try to seat a new screen and mis-align the digitizer connector a few times you will damage one or both ends. Take a look at the connector ends with a 5X loupe and you will see damage on one of both corners. If you see damage on one corner start the alignment of your digitizer connector on the opposite corner. If both are damage you will need to have a new connector soldered on to the logic board. A good test is do your new digitizer snap into place, if yes then you have a good connector.