A volt meter only gives you the no load voltage. A dead battery can have close to full voltage, but can't stand any load. Battery testers do this load test.
Put the battery under load and then measure the voltage. A suitable voltage torch bulb or 100 ohm resistor across a dead battery will be enough to drop the measured voltage to about zero, and won't take much out of a good battery in the time it takes to do the test.
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