I agree, if the battery is dead, don't worry about it. Leaving it plugged in all the time will have minimal ill effects if the battery is already dead. The only real ill effect of leaving a laptop plugged in all the time is that it wears down the battery. And since your battery is already worn, you don't need to worry. Anyway, your laptop will be obsolete to the point where it will no longer be usable long before you will burn out the circuitry.