My wife and I bought two Nexus 7’s recently.  The Nexus would not turn on.  With a little research I quickly found out that you can use your finger nail to take the back cover off.  So I gently popped the cover off and saw that the battery had shifted away from its connection.  I took my thumb nail and slid it back in to make the connection.  Then I took two Q-tips and cut the cotton ends off and wedged them in against the battery as to prevent it from sliding around.  Also I took some black electrical tape (Vinyl tape) and laid it along top of the location that I placed the Q-tips.  This would make sure that the Q-tips would not move along with the battery.  Then I popped the back cover on and pressed the power button.  Successfully, they both now power on. I can only assume that the battery connection came loose during shipping.