the charger uses so little 120vac and converts it to 12vdc, that 200ft 16ga cord would work in a pinch.
EDIT...after re-reading, I see you are using the house converter, and NOT an aftermarket charger.
the converter should produce 12volt power regardless if a battery in installed or not... so there is another problem elswhere
the following concerns the new triple stage chargers that do a much better job of optimizing the charging of the batteries...
here is the problem with dead batteries and modern chargers... for what is called safety, but more accurately described as "liability", the better chargers NEED to see about 9 volts for it to know there is a battery attached.. no battery, or a fully dead battery, NO OUTPUT....
the circuitry is so light in these modern chargers that running hard for so long in an attempt to charge up a fully dead battery would cause it to fry itself...
the REMEDY... use jumper cables to connect another battery up to the dead one. use your car if you dont have a spare batt laying around, then let the dead batt charge for 15 minutes...
then while the jump cables are still attached, connect the battery charger to the dead battery, and then disconnect the jumper cables... the charger will now work normally and charge the battery.