Your problem sounds very similar to what I experienced recently and posted about
here. There were some good advice both there and in
this thread. In the end it didn't help me, but maybe one of those tips might debrick your Kindle? It's definitely worth a try!
(I second 'charge for a
long time'. That was definitely
one of my problems, but in the end not the ultimate cause. And
long in this case means 'several days'. The SoC can get into a funny state where it pretty much just trickle-charges the battery, which can literally take several days.)
[aside]
The green LED can behave in weird ways. I never quite figured out what it means. I did see the 'green flashes' (two or three times) that you describe, and I also went through a phase of
very slow flashing (5s on, 5s off, repeat).
Is the LED behaviour documented anywhere?
[/aside]