I deliberately emphasized voltage rather than charge above because it is (notionally) possible for an M5653 or M5654 NiCd system battery to show nearly full (7.2+) DC voltage, but have anywhere from a few tens of mAh capacity up to full capacity. Of course, only a little capacity (charge) in mAh will not power the PB for any useful time. However, the backup battery (which holds only 30-50mAh charge) can be charged as long as the voltage between terminals of the system battery can reach about 6.5VDC or more.
If the system battery gets very hot during charge it is likely to be shorted internally, and should be re-celled or discarded. In any case, it is not likely to hold any useful charge or reach a useful voltage while it has internal short-circuits.
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If the system battery gets very hot during charge it is likely to be shorted internally, and should be re-celled or discarded. In any case, it is not likely to hold any useful charge or reach a useful voltage while it has internal short-circuits.
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