While driving battery light is on car dies, jumped battery, starter went bad, replaced starter, installed new battery, tested alternator by removing negative battery cable and car still runs, drove it six miles to Pep Boys, batter light comes back on, they tested the alternator, said that it was OK but said that the new battery was only putting out 300amp and not the required 700. Returned battery, new replacement battery, car starts fine then the whole process starts again. note AC will not shut off.

 

welcome to acurazine--we need to break these symptoms down a little bit, and get more info ok

jumping the car doesnt kill the starter,
it DOES put the hurt on the alternator as it tries to charge a dead battery--its normal job is much less work for it

bad starter can drain the battery, making it appear dead

you DONT test modern cars by removing the neg cable!!!--that hurts electronics!!

you DO have to drive with a new battery about 45 minutes with no extra load of ac , lights, tunes etc
let the alt bring the battery up to full charge like normal
The new batteries dont leave the factory at 100%, and sitting on a shelf allows draining

So you have to drive it to get it full- then run a machine based system test to know alt starter and batt are all good

what do you mean AC wont shut off?
the cabin fan? the auto temp selector? what??

after the car is shut off a radiator fan keeps running?
the driver side or passenger??
passenger side fan runs with ac ON
driver side fan is run by engine coolant temp and a bad fan sensor will allow fan to run 20++ minutes or maybe until battery dies