I concur with Meya, time to retire that one. As to why some still work and some don't: That's normal variations in manufacturing and use.
Plus, if you actually have an "original" Kindle, those had user replaceable batteries so it (the battery) might not be original. I'll bet a bit surprised if you actually have a first gen model as that was a long time ago. Wedge shaped? Round charging cable not USB? Image below:
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