Yes a 10 volt battery could be indicating a failed converter. Could also be an open connection between the converter the battery. Assuming the battery held 12.6+ volts after charging them I would consider the battery fine for what you need to run some jacks.
You will need to verify operation of the converter. Basic operation is 120 vac in and 13.6 vdc out. Need to dig in and verify with a voltmeter.
Although the jacks should run fine on battery power assuming the batteries are mostly full charge. You could have a couple issues to resolve. Need to separate the items and start testing.
