Based on the community response, there does not appear to be a standard way to run the Profoto B2 directly from AC power. The B2 is a battery-based pack system, so if you want true AC operation you’d likely need a different compatible pack/system rather than just the B2 heads alone.

For batteries that won’t charge, one possible issue is that they may be deeply discharged—so low that the charger’s protection/smart charging circuit won’t begin charging. A sometimes-used workaround is to briefly parallel the low battery with a good 12–14V source to raise its voltage enough that the normal charger will recognize it again. This can be done only with great care, since incorrect voltage, polarity, or handling can damage the battery or create a safety risk.

If the batteries have been sitting discharged for a long time, they may simply be at end of life. In that case, replacement or switching to an AC-powered lighting system may be the practical solution.