Your car probably has a bad/or some bad connections between the battery, the alternator, the starter, and chassis ground.
The battery will not charge without good solid electrical connections. The alternator connects with the positive battery terminal down on the starter, and and with ground on the left inner fender.
On my Taurus Wagon, the ground connection on the left inner fender was covered with cloth electrical tape at the Ford Factory (probably to protect it from corrosion. The connection was slightly corroded, and loose when I removed the tape to inspect it when I had a similar problem to yours.