I have almost exactly the same problem as well: If I have my phone off for more than a few minutes, the screen is mostly unresponsive unless I sleep and wake. It will respond to some touches but not most, and it’s bad enough that I can’t even swipe to unlock. I have not replaced the screen on my phone. Rather this issue started randomly one morning after sleeping on it. My headphone was pressing into the screen. A hard reboot didn’t fix anything. I also thought it might be something to do with capacitance, like sleeping and waking was discharging something. However I bet it is a faulty connection corrupting some controller, and sleeping resets it. If opening it up and wiggling around the connection works, I’ll post here.