I doubt the computer needs to relearn, esp if its all stock. When I had the stock tune in my car with the cam it would be a little off for the first couple minutes, but it would learn pretty quick.

If it starts off the battery, its not that problem. If you are jumping it and it will run with the cables connected, then shut off when you unhook them, then yes, it might be the fact that you aren't getting enough juice.

Sounds like progress at least- Will it run smoothly when you give it gas, or does it still cut-up and run rough?