My Nexus5 was doing the same thing. Turns out the connector from the Battery (the little Copper piece that sticks of the top of the battery) wasn't seated correctly into the phone. It needs to snap into the connector.
If you phone only flashes the battery symbol when it is plugged in, I believe that means it is getting power, but doesn't find a battery in the device. I removed the battery, and plugged the phone into my charger, and I got the same battery symbol flashing, and Android would just keep rebooting.