Sometimes charging problems are due to a temperature sensor calibration issue. This can often be corrected by placing your Kindle in a freezer overnight. Wrap it carefully to ensure no problems with condensation. After allowing it to warm back up try charging it again from a wall adapter.
The fact that your computer fails to see it may indicate other problems, possibly with the mainboard itself. It is also possible that the battery itself has failed in some manner.
If the freezer trick does not work for your case, you will need to open the unit and connect to the serial port to see what is going on. This requires the proper tools and ability to work with tiny, delicate, easy to damage connections on the mainboard. If you can handle this yourself see the serial jailbreak thread for the PW1 for directions on accessing the serial port.
Beyond that you could ask if someone in the forum can help, contact Amazon who will likely simply offer to sell you a replacement at a discount or offer it for sale on eBay or Amazon as a "not working, usable for parts" unit.
Dave
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