Beats Pill 2.0 Battery Replacement (Beats Pill won't turn on or charge)

My repair of a recent Beats Pill 2.0 that did not want to charge anymore. Apparently many, many people have that problem. Turns out it's one of the battery cells that's dead. Warning: features unremarkable consumer hardware that does not work. Vintage fans of my other superbly-engineered, milestone-setting hardware, move right along.