I would like to confirm the OP's results. My battery started doing the question mark thing out-of-the-blue, about a month ago. I tried unrooting, restoring to factory settings, I even tried older versions of the Nook software to see if that made any difference, and nothing. I tried to drain the battery, transferring files to and from the Nook over wifi, and even when I couldn't boot from low battery, as soon as I plugged it in I got question mark battery. Being in Canada, getting my Nook replaced is a huge pain, so I left it for about a month. Pulled it out today, just for the heck of it, and I got the Not enough battery to turn on screen (which was new, when the battery was in question mark mode it would always attempt to turn on, but fail silently as soon as power was removed). I left it plugged in for a few minutes, and lo and behold it booted up and displayed the charging animation on the battery icon. I charged it to full, and it seems to be as good as new.
So, for anybody else that has this issue, the fix seems to be to let it drain for a very long time, then recharge. Shortcuts don't work, and it isn't a hardware issue that needs replacement.