Re: start problem with 2004 Ford Taurus
It's either the battery, alternator, cables, bad connection or a major power drain somewhere.
Did Autozone even do a load test on the battery & check charging output voltage? Sounds to me the person that did the checking didn't know jack about what they were doing.
If you have a volt meter check the voltage while engine is running. If you have somewhere between 13 - 15 volts then that would rule out the alternator.