I'm working on the assumption that it's an issue with the connection between the display and the motherboard. Sometimes my phone works fine. Sometimes, the screen is dark and unresponsive. At other times, the screen is on, but doesn't respond to touch. And I occasionally get weird static and video artifacts on the screen. The rest of the phone seems fine. Alarms still go off, etc.
Like you, tapping or touching the upper left hand corner sometimes has an effect.
So I'm assuming is a connection issue. If anyone knows better, please correct me.