How come any of my car's elec working?tricity?

Ok it all started 5 days ago everything was fine untill one day while we were driving tha car had shake like it was gonna turn of f.. Then wen we had parked it & turn it off, all the power wasent working at all.. So then we started tightning it up .. So we checked fo a light n we had power so the next day we got a new battery frm auto zone n a day after it died again then I tried to give it a jump but nothing then if we let it sit there for couple of hours it ill have electricity.. So is it tha alternator? A fuze? Or wat? Please help me car experts please help me with this question?