It was indeed a dead battery. Not wanting to spend any money on this kindle (I already got it for free on facebook marketplace), I tried to disassemble the battery and charge the lipo without the bms (from the bare terminals using an RC charger). This seemed to fail, indicating a failed lipo.
So, I took a good cell I had on hand, which happened to be an LG MJ1 18650, and charged it up. Then, I soldered it to the bms battery terminals, and reinstalled the bms in the original plastic battery frame. This was then installed in the kindle.
I plugged in the kindle and had it charge via usb, and sure enough, after a few hours the green light turned on, and the kindle worked perfectly! The current setup is quite crude. The back does not fit on (the wires and the 18650 cell are hanging out!) but it does work. Now debating if I should buy a proper battery replacement since I have determined the rest of the device works, or if I should modify/build a new back cover and have it run off of this 18650 cell (which should offer about twice the original runtime).
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