Q: My truck will start with it jumped off but even with the jumper cables still connected it will immediately idle slower and die.

My truck has had a lose connection on the positive terminal for awhile but I have been able to move it a little and get a good enough connection to start it and it would run fine. Yesterday, my truck started right up and I started driving on the interstate. About 5-10 miles on the interstate my truck all of a sudden lost all horsepower and i had to coast to the shoulder. When i came to a stop, it felt like my engine was jerking under the hood so I turned my truck off and when i tried to start it again, it would turn over but not crank. I left my key in the ignition while i got towed to my apartment (not very far away) and my battery was dead when we got back. Now when I jump my truck off it will start right up but will immediately idle slower and slower and die, even with the jumper cables still attached. I can have my truck off with jumper cable attached for awhile, disconnect them and it will start but do the same thing. Am I looking at a bad alternator or could it be mechanical?