A blinking red light indicates that the battery has a low state of charge and it will not start the laptop.
Does the battery charge indicator light turn ON when you connect the AC adapter from a working wall outlet?
If the battery indicator light does not come on with the AC adapter connected, you either have a faulty adapter (make sure the power outlet is working), faulty charging circuit in the laptop or a faulty battery.
If you can, try another adapter ( ensure that it has the exact same power specifications and connecting plug ) and see if it will charge the laptop. If so your adapter is faulty and needs replacing. If not you have either a faulty charging circuit in the laptop or a faulty battery.
If the charge indicator does come on when you connect the AC adapter, allow your battery to fully charge, disconnect the AC adapter, allow your battery to "cool" for 5 minutes and then try to switch on your laptop.
If it turns on, you just had a low battery. You might have to keep an eye on it as it may be failing, i.e not holding its' charge. When your PC is running, double click the battery icon or power cord icon (if AC adapter connected) in the taskbar to monitor the state of charge
If it does not turn on after charging the battery or you get no indication after after a few hours that it is fully charged try connecting the AC adapter with power connected and turn ON the laptop and see if it starts. If it turns on you have either a faulty charging circuit in the laptop or a faulty battery.