My iPod does not work without direct power

I generally use my ipod in my vehicle and it is constsntly plugged in. In the past few days i noticed that when i shut the truck off for a few minutes then start it back up again the ipod would start on a new song rather than where it left off. So i brought the ipod into the house and noticed it would not come on so i plugged it into the computer and no responce on either end, i had a dimmly lit ipod saying "please wait low batt" with a spinning icon under it. I then plugged it into my ipod stereo and it works fine with full functions and shows battery light green with plug icon in it. As soon as i pull it from the stereo it goes off with no responce. It sounds to me like the battery is not holding a charge but as soon as i plug it into the stereo the battery light shows a full charge.

Thank You, Curtis