Oldsmobile/Buick Repair: 1993 Buick LeSabre battery drain, buick lesabre, volt light

Question
I recently have had problems with my volt light coming on and all the lights in the car dimming terribly.  I took out the alternator, had that checked at AutoZone, it was fine.  I then took out the battery and had that checked, it was dead.  Great.  So I put in the new battery from AutoZone and within 25 minutes of driving, it was dead again.  Why is the alternator not charging the battery?  Also, when i then connected a charger to the battery, it stated that the battery was fully charged immediately

Answer
HI JJ,ONLY TWO POSSIBILITY,S HERE  NO 1 A FUSED LINK BURNED IN TWO COMMON ,THE LINKS WILL ALL BE TOGETHER EITHER ON THE STARTER OR THE FENDER NEAR THE BATT.IF THESE ARE ALL GOOD.WELL THEN THE TEST WAS PERFORMED WRONG AND THE ALT IS INDEED BAD.IF NO LINKS BURNED NO FUSES BLOWN NO WIRES LOOSE FROM THE ALT .THEN TAKE IT OFF AND GO HAVE TESTED SOMEWHERE ELSE.ONE OF THESE WILL BE THE PROB.PLEASE   VOTE FOR ME TY BILLYMAC