Just registered to say that I had the same exact problem. I suspect the cause was the battery, which was so empty that it may have had difficulties starting to charge. Whenever I plugged in the charger, the orange light would stay on for only a few seconds and turn off again.
How it worked for me (don't know which part did it)
- I opened the case, took out the battery, put it on again (the green light blinked for a second, which gave me some hope).
- I tried charging, same situation as before opening the case. Connected it to my computer, same as before (it was not recognized).
- Got mad, continued to push the button (still plugged to my computer), but this time from the inside (the case was still open), with my nails. Strange thing happened: everytime I pushed the button from the inside, the orange light turned on for a few seconds (I don't think the same was true when I pushed the button normally). I continued to push it many times, as I thought that maybe it was charging only while the light was on. After some attempts, lo and behold, finally the green light decided to show itself!
- I just let it charge and after that everything looks fine!
Hope this helps. I've been looking through forums for a solution to this, but it looks like people mainly gave up and returned the Kindle. Couldn't do that since I don't live in the USA and a friend bought it for me in the store there.
Cheers!