If the screen shows the battery indicator when you plug it in, then either the battery is bad or your charger is bad and the phone is not charging properly. As staff at a GNex forum, this is only the second time I have heard this, and the following solved the other problem:
I would make sure the charger is the one that came with the device (I have a few LG micro-USB chargers that fit, but do not charge the device) and wait about 5-6 hours to make sure it charges completely. If it still will not power up, try another battery. (the GNex uses a battery that includes the NFC antennae right on the battery so if you plan on using that, you will need that in the permanent one)
If a new charger and battery do not solve the problem, it may be an issue with the wiring to the battery/charging circuit. A replacement may be required.