Definitely try it with the cable as well; you can rarely assume the battery has a charge.

Found this at "howtogeek.com:"

"Tablet Won’t Power On or Charge

If your Nexus 7 appears completely frozen and won’t power on or even charge, the most obvious solution is to pull the battery and reinsert it. However, the Nexus 7 doesn’t have a user-serviceable battery.

Instead of pulling the battery, hold down the power button for 30 seconds straight. You may have tried holding down the power button already – but you won’t see any results until you hold it down for the entire 30 seconds. This process fixed a Nexus 7 that refused to turn on or charge."