DIAGNOSIS Your thermostat has lost all power. This isn't a software crash; it's a power issue at the wall. The most common cause for a sudden, complete blackout is the HVAC system's fuse blowing or a tripped safety switch.
FIX First, check your home's main electrical panel for any tripped breakers related to your furnace or air handler and reset them. If that's fine, you need to check the furnace itself. 1) Turn off the power to your furnace/air handler at its own switch or at the breaker. 2) Open the furnace door. There's usually a little 3-amp or 5-amp car-style fuse on the control board inside. 3) Pull it out and check if the thin wire inside is broken or the glass is cloudy. 4) Replace it with an identical fuse from an auto parts store. Turn the power back on. Your Nest should wake right up.
IF THAT DIDN'T WORK The issue could be with the Nest's baseplate wiring. Turn the HVAC power back off, pop the Nest display off its base, and check that all the tiny wire connectors on the base are pushed down fully. Sometimes one gets loose and breaks the 'C' (common) wire connection, starving it of power.
HEADS UP If you don't have a 'C' wire connected at all, the Nest E tries to steal a tiny bit of power from your system when it's off. In some systems, this can eventually drain the internal battery and cause a black screen, especially if your system doesn't run for long periods.