So I was having a lot (a LOT) of trouble with my Kindle Fire after I accidentally dropped it. The day after I dropped it, I put it down and went to go do something else, and when I came back, it wouldn't turn on! So I plugged it in, and, yay, it worked! But THEN I saw that there was a question mark over the battery symbol, and when I unplugged my Fire, boom, it went black again.
This went on for about 3 days - me plugging it in, seeing that the question mark was still there, unplugging it - before I finally got the sense to look around these forums.
And... yaaay! I found out how to fix it! According to one of these posts (I forget which one), when my Fire dropped, the battery sort of jiggled and suddenly it wasn't hitting the right places to make it work anymore. So, while plugged in, I tapped the sides of my Fire with my palms medium-hard about 3-5 times. Then I unplugged it and plugged it back in. NOW IT WORKS!!
I really hope this method works for somebody else out here in cyberspace. I have no guarantee that it WILL work, but it's a heck of a lot better than doing a Factory Reset or (God forbid!) buying a new one.
If this worked for you, can you reply to this post? Thanks!