No electricity going to thermostat
With certain versions of the nest thermostat they require the C or common wire for operation. The nest thermostat needs 5 wires to accommodate the extra common wire. Check to see that how many wires the thermostat wire is. You may be lucky and have the extra wire tucked in behind the thermostat.

Another possible issue, if you do have 5 wires hooked up at the thermostat is the C wire may be disconnected at the furnace control board as it was not needed for the old thermostat. If this is the case you would have to open the furnace and add the C wire to the C terminal of the control board.