When I installed the Nest in my home, there were a few initial issues. First, the display wouldn't come on because the battery would never charge. As a first step, I charged the Nest via USB. Then with the display installed I tested the A/C unit. The A/C would come on, but only for a second. Also, the battery drained after only a few minutes. I did a little research and realized that I would probably need to use the C wire (or "common" wire).
The C wire is not typically necessary but may be required in some systems. In order to connect the C wire, I had to go into the attic and connect the C wire to my controller (see the image). Note that mine is a dual zone controller. After that I connected the C wire to the Nest base, and plugged the display back in. The display immediately indicated that it was charging, which it didn't do before. After a few minutes the display came on and I was able to configure the Nest.