If no power to the nest then I would check the power to the HVAC system.
If the breaker/switch is off then power won't be supplied the nest. Or
if they have there own power feed from a transformer check that.
Depending on the age of the compressor, it may be low on charge. If you
have an old thermostat you can swap try that. Otherwise a call to the
local HVAC folk might be needed.
If you have 2 stage cooling then you should have a wire in Y1 and Y2. If
you only have 1 Stage cooling (typical) then the y2 is not used.O/b on
my E stat is my 2nd stage cooling since I don't have the y2 spot. You
would program the o/b port in equipm...