Its normally the Power input jack is bad or the Charger of the laptop.
The LED flashing just means that it knows that there is a battery there, but it doesn't have enough power to run the laptop.
Your battery has died because your power cord has not been supplying power to your PC. You would not be aware at this point that the laptop was running from the battery. The battery has just run out of charge.
The best thing would be to do is see if anyone has a battery like yours and try it with the new battery fully charged.