1994 Other Nissan Models No power loss of power won't stay s

I just bought a used Nissan Quest minivan and it had been sitting for a while. The guy said he replaced the fuel filter recently on it. The battery connectors on the side are not real tight so there is not a good connection. So we tried to get it connected as good as we could to get the car home. It was low on gas and it stalled with the gas station in sight and I could not get it started again. We had to push it in to the Gas station. After putting gas in it the thing would not start because the battery was dead. We got a jump start from someone and it started right up. We started driving down the road and it was like the thing had no power and it would sort of sputter and act like it was going to die. I tried using the gear shift to actually shift it down to second and it seemed to run a little better. We finally were not able to get it to go any further and after trying to start if numerous times the battery is dead again. I am wondering if the battery is the issue or do we have a bad starter or alternator.

Any advice would be helpful. I plan on getting correct cables on battery and possibly changing to new battery.