Data recovery from old phone with unresponsive touchscreen

My elderly neighbor held onto her Motorola Moto E (2nd Gen) for years till it recently stopped responding all of a sudden to her touches. It still charges fine and the display exhibits no issues, but the touchscreen is totally unresponsive despite repeated reboots. I'm guessing the touch digitizer is dead? Anyway, I've convinced her it's pointless to waste money repairing it and to simply get a new device. Since there weren't too many apps in use (most apparently stopped working over time on what must've been either Lollipop or Marshmallow), those aren't the issue here. What is required is to extract the bare minimum but very important data from the phone like **pictures, videos, contacts and messages (SMSes)**, and finally import everything into a new Android phone. So my question is, is any of this even possible with a completely unresponsive touchscreen? And if so, how?