The B&D needs the battery to have 4 or so volts or it won't run, as you saw there. To beat that, first apply some charge from the dumb charger or jumper cables or solar, then start the smart charger and it will get going.
The B&D has a way better charging profile so it is worth using that once it can run.
You might also notice on a very low battery that the charger only does really low amps, so you might think something is wrong. Let it keep running and the amps will slowly increase as the battery comes back to life until the charger is at its max amps. Then after that, the charger will do its normal profile.