1994 Lincoln Continental

My car died lastnite and when I jump started it I drove it up to the gas station and the battery died again. I tried to jump it and it wouldnt stay charged. When the cables where on the battery everything worked lights and all. But the car wouldnt turn over. Then when the cables came off the battery completly died like it wasnt charged. I dont know if its the battery or the alternator but if you have any sugestions it would really help.