DIAGNOSIS The thermostat is not receiving power from your HVAC system's wiring. The Nest has no internal battery to run the display.
FIX Remove the display from the base. Check the wire connectors on the baseplate are fully inserted. Reattach the display. If the screen remains black, the issue is at the HVAC system.
IF THAT DIDN'T WORK The common 'C' wire may be disconnected or missing. A Nest can sometimes run without a C wire, but system cycling may drain its internal battery. Open the equipment and verify the C wire connection at the furnace control board.
HEADS UP If you lack a C wire, enable the 'C wire detect' setting in the Nest's Technical Info menu. The thermostat may need to charge for 30+ minutes via USB before re-mounting.