Some devices (I don't know about the Nexus 7, but I think it will be about the same) only charge when they have still a little charge left on their battery, because - believe it or not - charging happens electronically. So it can be that your device has absolutely no juice left to run. An example of such a device is the BlackBerry PlayBook (not Android) where this trick works when your tablet doesn't want to boot.
But there is a simple solution for that, which can take some time. Try to keep your device awake for as long as possible, even if that means you have to restart it a couple of times. Of course you do this while your charger is connected. After you have restarted it a couple of times, it should normally boot up. I expect it will take about 7 or 8 boots for the battery to be charged at minimum level again. After that, make sure you keep the device connected long enough so the battery is fully charged (have a look in your user manual how long it is recommended, most tablets need about 8 hours).
Another option is that your device just needs a little more juice to start. In that case you should leave it plugged in for some time (I recommend at least an hour) before booting.
tl;dr: Two options you could try: 1) Just keep restarting it, after a while it will start as normal. Recharge the battery for a long time (probably around 8 hours). 2) Leave it plugged in for a long time before restarting