Nexus 7 stuck at Google logo, and system recovery, and OEM locked Short version:

Normal startup: Stuck at Google screen.
Unlock bootloader: Stuck at the selection.
Recovery mode: Stuck at Google screen.


Long version
My Nexus 7 (2013) had always been fine, and I liked stock Android very much, thus saw no need to unlock the bootloader. When the 5.1 OTA came, I updated my N7 and it started crashing and restarting on its own. One day, it restarted again and got stuck at the Google screen.
Of course, the first thing I did was to get the Nexus Root Toolkit, and tried flashing stock ROM. Of course, it didn't work since it was OEM locked. When I tried to unlock the bootloader, I was prompted with the screen asking if I want to unlock and wipe all data. I selected unlock and pressed the power button. Then it froze (I left it for 8 hours, plugged it into a power outlet).
The next logical thing to do was to start recovery mode in the fastboot to do a factory reset, except it simply switched to the Google screen and was stuck there.
I've read many articles, but it's always one of the three issues I have. They often refer to using a method that involves an area where it's affected by the other problems.
How to recover from this situation?
This sounds like a common bug that has been reported on recently by Android Police. To summarize:


  Affected units stop booting at the "Google" logo screen.   Attempts to
  unlock the device through fastboot fail at the "erasing userdata..."
  step, leaving the devices locked.  Some users report successfully
  flashing factory images on unlocked devices, but this still doesn't
  fix the problem.  There are mixed reports about starting up in
  Recovery, with some users complaining that the Nexus 7 freezes, and
  others being able to get in to perform some maintenance.


There are no know solutions at this time. Sorry to bring bad news. I hope I'm not right.