I had a similar thing happen with mine. I have only had my Nexus for a couple of months, its the 2013 version. It's my first android tablet, having only had Fire tablets up to this point. A few weeks ago it was just dead. I am guessing something was running. So I plugged it in and still nothing happened after a while when pressing the power button. After a few hours I don't know what I did because I suddenly had some strange screen with start here and some robotic looking graphics. I freaked out. There was reboot system and some other stuff on that screen I just don't recall anymore.
On that screen I held my breath and pushed where the arrow pointed with start.
. Hasn't happened since. I must have pressed some combination of volume and power maybe to initiate some boot screen. Hasn't happened since.
But like Harry, I wouldn't have known what to do if that hadn't worked. I guess I am used to easy kindle stuff, I never get to see the "innerts" so to speak on it.
Haven't had any other issues with the device other than the occasional freezing of the screen which only goes away if I turn the device off and on again. I don't know though if that is an app or a Nexus thing.