Battery will not stay charged

Well, I just bought a car of a friend he put a new battery in the car and an alternator just a year ago before he got his new car and it has been sitting for about a year. Well, we went to start it and it started then when I went to drive it, it moved a couple feet then shut off and I tried to start it back up and it would click when I turned the key over like it was getting power but all the lights were on and everything. So we figured I would try to replace the alternator and see if it would work. I replaced it and it started when we jumped it with a jump pack and it ran fine for a couple minutes then the engine started shacking and making noises and started stalling and it started shutting off so he tried to keep it running by throttling it a little and it tried to stay running but the engine shut off. We tried to start it back up and it would not start all It did was click when he turned the key over like the battery was not staying charged. I do not know what the problem is. I would like to know what it could be so I can replace it and try getting it running so I can have it for work.