The best thing you can do at this point is take the unit to a repair center. If that is going to be too expensive, then get rid of it. It sounds like it has a serious, and potentially dangerous, electrical fault. I would not plug it back in until it has been looked at by someone.
if the ac adaptor shorted out then it may have taken the mb or charing board if this laptop has a daughter board for power with it. if your lucky the power plug on the laptop the solider joint is broken. it a standard pasrt that you can order from digikey. you just have to soilder to old one off and soilder the new one on if it out of warranty.