That reminds me how I once dropped my phone into a vat of industrial solvent; not for very long, but enough for just a drop or so to enter via the charging port. The substance gradually separated layers of the screen. Touch worked, but the big black blob in the OLED eventually overtook the entire screen. Before it went completely dark, I enabled screenshot upload (aside from camera roll) to Dropbox. Then it was just a matter of taking screenshots and measured taps to turn the phone into a very fine GSM modem/wi-fi router as I looked into getting another phone.

Rooting with a completely melted screen would be a little harder, but hey, maybe rooting could be done by following the instructions step-by-step with a little faith, and then post-root the USB might work with an external portable monitor? I'm sure it's a solvable problem.