From my experience: the moment the old thermostat is working then you have power to Rh (the old thermostat is using its own battery power and the only thing is doing is to route the power from Rh back to the furnace on the wire based on your selection: heating, cooling, fan on manual mode) but if you miss the C wire, which is the ground, then Nest will not power up if it has a drained or a new battery that was not charged in advance.
If you remove the Nest and have access to the backplate with the wiring, then you can measure Rh wire (only if the furnace is powered up – of course is not running since the thermostat is removed) against any others and it should be 24 Vac (AC and NOT DC this is the most important thing to remember since I was confused by 2 people and this site included where they mention only 24V only – big mistake). Since the electronic boards/components are running with DC voltage I thought that I need to measure it in DC and you will get almost nothing, plus the chance to mess up with the furnace board.
BE AWARE (again from my experience): The C wire in my system was cut, both ends by the installers 22 years ago and the NEST ran out of battery juice after few years, this very Sunday, if this is missing. After I connected the C wire and then learned that I need to measure in AC mode I have detected that the wire is still broken. I found another place where the builder has connected 2 cables (did not run 1 single cable from end to end) and they connected only the black wire and the white one (C) was cut again and needed to be reconnected. After the last fix, I got 24 Vac at the backplate of Nest, and after plugging in the Nest itself it finally started.
Hope this helps even if is long answer that encompass the reason of the fixes and possible other issues.
