I had a Kindle in for "repair" over the weekend, customer said it was completely dead, another place had told her it was water damaged.
Turned out the charger (original) wasn't high enough amperage to start the charging process when it was completely flat.
Fiver for a 2A USB charger later and one VERY happy lady.
The battery on a Kindle shouldn't be failing yet unless its one of the early ones.
What is the actual problem that you're having with it ?