Late yesterday, my Nexus 6's battery died. When I charged it and turned it back on all seemed to be well. The start-up animation came on and I entered my "swipe code". The screen was black, but I didn't think anything of it until my alarm went off this morning. I was unable to turn it off because the screen was black and unresponsive. I held in the power button and the "Turn Off" Menu showed up so I restarted my phone. It did the same thing - starting animation, entered "swipe code" and then a black screen. I searched Google, and some people had success booting in "Safe Mode". That caused the same result with the exception of he words "Safe Mode" in the bottom left corner. I also tried booting without the SIM in and same result. I have called the phone and it does vibrate, but it is not responsive to answer. Is there some way to recover the phone without a factory reset? Just as an FYI, I am running the newest version of Android Marshmallow available for the Nexus 6 with the March Security patch.
Sounds like a software bug.
No real solution here, but a plan of attack toward discovery of the culprit(s).
Try to pull the battery, and restart. If the battery is non-yankable, it'll have to discharge fully to kill all processes. I usually expedite this by leaving it within reach of my neighbor's WiFi, where it exhausts itself trying to Connect...Connect...Connect.
Charge some, and restart, until the buggy situation becomes clear to you through experimentation, again. I say charge SOME, because if you charge fully, it'll require double patience to discharge again.
Let us know what you find out. For myself - I believe this occurred when the Amazon Kindle app was trying to download books that I sent to the device via computer. It MAY HAVE STILL BEEN DOING SO WHEN I LEFT THE WIFI AREA (pure supposition). The first time did not occur to me, but the second time it did it (for a trip), and I recalled it happenned roughly similar to the first occurence. From now on, I'm careful to gauge full downloads while the device is awake, and Close the app fully. Hasn't recurred in a few months.