In cases where your Kindle battery just will not take a charge because it is TOO discharged, you might want to try this little trick to wake it up so it WILL take a charge:
This video shows a cellphone battery being revived, but the same trick may work on a Kindle battery. It is certainly worth trying before discarding an otherwise "dead" battery.
Do not apply the uncontrolled charge for long (more than about 10 seconds) to prevent danger from a Lithium fire. Better to do this outside, or at least on a fireproof surface.