On an iPad 2 which is partly responsive touch, how to check if digitizer cable or rather, connector is broken?
Sadly the best way to check would be with another whole display assembly. It sounds like it could be the actual digitizer layer (sits under the LCD display that is covered by the gorilla glass) or at least part of it that's broken. If the cable was the issue  if expect the whole display to stop responding to touch. Good thing is the part is easy to find, ifixit should be able to help with that and any tools you might need.