Of course, the other (theoretical) possibility is that the battery is good but your 830B impedance is very low. Again, if my calculations are correct, for the figures you report, the input impedance of your 830B should be about 4.2 ohms (for a battery internal resistance of about 1 ohm). In this scenario, the current going through your instrument should be about 2.2A.
If your 830B measures other voltage sources with no issues, this scenario is very-very unlikely.
Just for fun, why don't you measure the current passing through your 830B while you measure the voltage across the battery terminals? Connect your AN8008 (on A/mA) in series with the 830B (on 20V) and with the battery and read the current on AN8008. If you measure something of the order of ~10-20 uA, the 830D meter is good, the battery is bad. If you measure something of the order of ~2A, the battery is good, the 830M meter is bad.