6.1.2 update bricked my iPad Mini - White Screen of Death

Question

I updated to 6.1.2 over wireless.  Shortly after, I noticed the battery was draining extremely fast.  I followed a suggestion I found here to let the battery drain to 0 and to reset my settings under Settings>General.  When the battery was about 50%, I shut it down completely as I wasn't using it and so that it would charge faster (not using battery on standby, etc).
I let it charge for about 4 or 5 hours.  When I turned it back on, I got a bright, solid white screen and then it shut off... or so I thought.  The device remains warm, as though it was in regular use, but the display is OFF - NOT blank, OFF.
It will not go into Restore or DFU mode, it will not turn back on, it will not do anything.
Waiting on an Apple call in the morning, but once it is replaced, I doubt I will purchase another Apple product, considering the sickening irony that my iPad was functioning fine prior to the update and the VERY UPDATE MEANT TO IMPROVE BATTERY LIFE ACTUALLY KILLED MINE to begin with. 
I have very weak faith in Apple at the moment.

Answer 1

Guys, my ipad mini just had the exact same issue yesterday.
It was recently updated (about 1 week ago) to 6.1.2  and since yesterday it just turned into a brick (black screen, no reaction whatsoever,...) .
I tried different chargers & different USB-ligthning cables without any result. Somehow it seems the battery does not have any juice anymore and won't charge either.
My bad luck was that 4 months ago my daughter had the ipad mini dropped on the floor and the screenglass has a small crack. It did not affect any functionality and still worked fine untill yesterday. I went to an official apple store and they told me that the warranty doesn't count on the complete ipad since the screen is cracked/damaged.
Explaining that the crack had nothing to do with the current issue we have did not help.
Now I'm standing here with a 6-month old product which has no warranty and is as death as a brick.
Thanks to Apple!