WHEN A BATTERY DIES IT RUNS OUT OF CHARGE
WRONG!!

Many people confuse charge with energy. When a battery is new it contains stored up chemical energy which can drive charge round a circuit. every atom has charge and the number of atoms in the battery do not change. More to the point, the actual electric current involves a flow of charge, but the battery does not run out of these charges either.
There are charge carriers all over the whole circuit, in the wires, the battery, any device connected to the circuit etc and when the switch is closed to turn the current on ALL the charges throughout the whole circuit start moving at once. Over the whole period of use, the number of charges which go out of ONE end of the battery is the same as the number into the OTHER end.
you can imagine it like a piece of string stretched round some pulley wheels, when you turn on (pull the string) the string everywhere starts moving at the same moment.


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