Symptoms:

1. Nexus 7 won't power on.

2. Battery icon doesn't show when charger plugged in.

3. In a dark room, you can see backlight is turned on. If you hold down power button for 30 seconds, you can see the backlight power cycle.

Solution:

1. Hold down both volume buttons (Press the center) and plug in charger (while holding the buttons). Hold down for 40 seconds.

2. Hold down power button 40 seconds to boot Nexus.

In the future, don't let battery discharge too much.