What sort of charger is it?
Plain "dumb" transformer/rectifier? Regular older type? More recent ?
Dumb transformer/rectifier types ought to just work, nit much to go wrong except the rectifiers, the transformer is pretty reliable.
The older standard types have SCR and some voltage circuitry to control the charge, obviously any of that may go bad, hard to say what.
Newer ones have more complex contriols, and may refuse to charge unless the battery is at a reasonable state of charge to begin with. If too low it will just sit there and not do anything. The 10.8VDC is still "within range" if that is battery voltage, as I suspect. Most newer chargers ought to charge that,
Your sparks might be either from current going OUT to the battery, OR from a load put on the battery ny a dead charger. No idea which. Is there a meter for current? if so, does it show ANY wiggle at all?
EDIT: One failure mode for batteries is to go open, or nearly open. At that point, they may not accept a charge, and will have very low capacity, if any. In such a case, they may provide "sparks" as you noted, nut have no real ability to really power anything or to accept a charge. Before giving up on the charger, try another battery that is known ok.
Chargers are cheap, it's hardly worth fiddling with them these days, unless it is a special one that cannot easily be replaced.