You can get a replacement battery for very cheap here.
http://www.powerbookmedic.com/Amazon...y-p-23506.html
I will let people who know what they are talking about respond, but I have read before that sometimes a dead battery can corrupt the internal memory, while it is booting up and shutting down?
Unfortunately, the only way to really check that is to hook up serial port internally to the kindle.
A couple of clarifying questions people have asked in the past.
If you hook it up to your computer, does anything show up in device manager? Either the usb drive or a serial recovery device?
You can use this to monitor usb devices by connect time:
http://www.nirsoft.net/utils/usb_devices_view.html
After you have charged it for 48 hours, if you unhook the cable and hit the power switch, does the light flash at all?
Does the light flash when you hold the power button for 40 seconds while it is unplugged?
My understanding of the method of recovering from dead battery is this.
1. Put the kindle n a wall charger for 48 hours.
2. Press the power button once
3. Leave the kindle on the wall charger for another 48 hours.