2001 Chevy Malibu alternater

Electrical problem
2001 Chevy Malibu 6 cyl

Having problems with the alternater charging battery. The old alternater tested good at the auto parts store but I still tried a new one. The car will start when jumped but once the jumper cables are removed the car trys to run on the battery and eventually dies. Im wondering if there is a computer issue because Im not used to working with computer driven cars. And money's tight. Any advice?