One of mine has gone flat, and won't charge with the supplied charger. Turns out not to be too difficult to strip; four concealed screws, a clipped-together case that needs to be forced quite firmly, and WD40 applied to the sticky foam that holds the battery pack into the case.
As I think TNP guessed in a previous discussion, these contain three cells in series for the main "jump start" supply. There's also a switched mode power supply that provides the various higher voltages required for laptops, as well as the supplies to the "torch" and the "emergency flashing red" LEDs. No *obvious* sign of why it won't charge.
It turns out that the batteries can be charged directly through the big "battery clips", and it is currently sitting on my desk being fed from a small (half amp max) lab power supply. It was taking 300 mA but has now dropped to about 150 for some reason. Supply is giving about 10.5 volts. For obvious reasons I am being gentle with the batteries, not using a car battery charger for example! But as they are about 125 x 45 mm and the stack is 20 mm thick I can't believe that half an amp will bother them.
It looks rather like one of these