Why does a phone's touchscreen 'completely stop working' when your fingers are wet or sweaty?

Because water changes the 'electrostatic capacitance field' on the screen's surface! Modern smartphones all use 'capacitive touch panels.' The screen has a dense grid of tiny conductive pathways at the bottom, which are normally energized to form a stable, weak electrostatic field. When your finger (a conductor) approaches or touches the screen, it draws off a small amount of current from that specific point, allowing the touch chip to precisely calculate your finger's coordinates. However, when your fingers are covered in water droplets or sweat, the water spreads across the screen's surface, forming a conductive layer. This causes the current in the electrostatic field to be 'diverted' over a large area by the water droplets. The touch chip instantly becomes unable to distinguish which point is being touched, effectively short-circuiting due to this 'moisture short-circuit' and ceasing to function!