The blinking light is, as the previous post said, a factory installed alarm system. It will activate any time you shut off the car, remove the key and lock the doors electrically. If you lock the door mechanically using the lock that's at the top edge of the door, or leave the car unlocked, the alarm won't arm itself, but why would you want to to that?
If your car won't crank, and your battery is going on 9 years old, then it is definitely time to replace the battery. If it still has problems cranking, look for corrosion on all the wiring leading from the battery to the starter motor.