Okay, I decide to measure the voltage on the battery (the pins are labelled). Zero, zip, nada, nothing. And more suspiciously, it is a cheap LiPo battery (like used in R/C toys) and its wrapper is "puffed" -- a sign of an expired LiPo. That explains a lot. I will try leaving (-) and (T) connected, but wire a 16850 lithium cell (like used en-masse in Tesla cars) to (-) and (-) on the kindle (leaving battery + disconnected). The (T) will be needed by the kindle boot code to assure it is connected to a "genuine" amazon battery. [Except the battery I2C (or whatever) may also need power from the battery? We shall see...