1991 Nissan Maxima My car only runs with a full battery

My car died on me. I tried starting it back up but it wouldnt start. I got a ride from a friend to oriley to get my battery recharged. they said it was still 75% full but they charged it anyways. I took the battery back to the car and the car started up first try. I went home. The next day I decided to take it back up to Oriley to see if they knew what was wrong. they tested the alternator and said it was bad. I drove it home and took the alternator off. I got a ride back to oriley and they said that the alternator was fine. I dont know what is wrong with my car. can someone please help?

Thanks