Then the alternator needs to be looked at asap But I even took the cable off alternator and car stayed on which meet alternator in good right?
Edit: If you took the cable off the alternator, then you disconnected the alternator so you didn't test the alternator at all. As a quick test only, removing the positive battery cable at the battery and the engine stays running means the alternator is charging. Do not run the engine more than a few seconds like this, and even then a voltage spike can wipe out your car's electronics. Much better to get a charging system tester to check things or at least borrow a voltmeter.
Something is on pulling power from the battery. Can be any light on the car or a stuck relay.
What brand is the car?
The battery light references more than just the battery. It represents the entire charging system of your car. They may be something wrong with the alternator or any of the wiring associated to the charging system.
There no better brand of battery for older model vehicles lite the duralast. This battery by autozone is the top battery to start a old high power car on the first try.
Alternator is no longer working properly.
Keep the car light on
The car light? YES! Leaving your car light on WILL make your battery run out. Things like leaving your car door open if the light is on because it is open will cause the lgiht to Mae your car battery run out. There is a big difference between shorted out a car battery and running the battery down. Lighting in itself won't short a battery out but will run it down.
the battery light means that your battery is being charged properly. so let it light.
The the alternator is defective.
Napa 84 series
The price you will pay for a car battery, will depend on what type of battery you want. you can buy a no name battery, or you can go with a brand name battery. Which would cost you more
its the alternator if the car is running with a battery light on. but check fuses first