Sounds like the alternator. The battery has nothing do do with the power of the car while its driving, it is used only to start the vehicle. the alternator runs the car once started, if the cars electronics are fading out while driving chances are the alternator is not butting out the 2 volts(+/-) that it should be, and it is now going to the battery for additional power, draining and damaging the battery.
Take it back to autozone and have them do an alternator test, and a load test on the battery.
I know not with what weapons World War III will be fought,
but World War IV will be fought with sticks and stones.
- Albert Einstein