I'm assuming that your "12v D cell battery" is a standard 12v DC automotive starting battery.
Since the battery needed so much water I'd think that the plates dried out and shorted out. 11.4v is a pretty well discharged battery though not completely drained.
If you have a battery hydrometer check each cell. I'll bet one cell is bad. Failing that, disconnect the cables from the starting battery and charge it overnight with a decent battery charger. If it doesn't take a full charge (12.6v or so) or if it takes a charge but discharges quickly afterward it's toast.
Most auto parts stores will do a load test for free, they'll also be happy to sell you a new one.