A couple of things: regardless of the battery age, if its state of charge is such that it can't feed at least 12volts to the car, it alternator won't charge. You must start with a fully charged battery, or else get a boost start. Once running, check the voltage across the battery terminals with the engine at fast idle. You should see around 14 volts if the alternator is doing its job. If you don't, the first thing to check is alternator drive belt and tension.
If you satisfy these conditions but find the battery going slowly flat, you have to suspect sneak current discharge due to faulty components/ wiring problems.
If you have any aftermarket stuff on your car, these are the prime suspects and should be isolated/ unplugged.