my 2002 buick lasabre keeps cutting off while drivng

while driving my car shut off and the battery symbol came on so  took it to the
auto parts store the battery check showed i needed a new battery they also
jumped it and checked to see if it was the alternator they said that it was fine
so i went and purchased a brad new battery . Was going to the store and 10
blocks later the car shut off again and showed the same symbol what else
could it be .