there is a very good possibility that when the alternator was tested they only tested for alternator output and did not do a diode test. A diode is like a one-way valve for electricity that only lets the eletrical current flow in one direction. When a diode goes bad the alternator will still charge at the same rate but when the car is shut off electrical current from the battery can flow back out through the alternator circuit and drain the battery. Over time that continual drain can kill the battery. If the battery is new because it was running down then the probability that the battery (charging system) light is indicating a bad diode is even greater. You will have to repalce the alternator to replace the diode. There is a test for the diode that can be done but you'll have to have the right tester to do it on the car. Most parts stores can test it if you take the alternator off the car and bring it to them.hope that helps