I had batteries go flat. No reading on BM monitor .Trickle charger wouldn't touch them. Took them back to where I got them and they charged them with some huge charger. Been fine since.
If the light is off when the mobitronic charger is plugged into the wall but disconnected from the batteries, and it stays off when you connect it to the batteries then my first guess would be that the battery's resistance is too high - i.e. yes, too deeply discharged, Try charging for some time with an olde dumb charger or for a few minutes (think that'll be long enough? maybe an hour or two?) with an alternator.
My batteries are knackered after I carelessly allowed them to get too low, but are very usable with (I guess) 50% of their original capacity.
The other way to do it is to have a charged battery and connect it in parallel to the flat batteries - a pair of jump leads will do - and then put the charger on. The flat batteries will draw on the good one and there will be enough current in the system to get it all charging. Have done this in the past on flat batteries on our old tractors when you used a pull stop to kill the engine and someone might forget to switch off the ignition and drain the battery flat.
Its a problem with todays smart chargers .... they default out if voltage is too low ....
Solution is either :
Old fashioned dumb charger that just puts out regardless ....
or
Parallel a reasonably charged battery with the low one - then connect charger ... the second battery will basically cheat the chargers system into thinking battery is fine ... once its come up to about 10v ... the second battery can be removed .... and low battery should continue charging.