2006 Ford Taurus checked battery and alternator and car sti

i was driving and the readout sail check charging system and then the battery light came on and then the car died, a while later it started up and i went to autozone and they checked the battery and the alternator , said it was fine, if you take the positive battery cable from the battery the car kills, it is still doing it but the battery light doesnt come on, the computer shuts off and the car dies, and will later restart, what could be the problem