4G batteries the same as 3G?

My 4G battery recently got fried. I'm pretty sure it's just the battery because it does not turn on unless connected to my Mac. At that point it mounts, is fully charged (it says), and I can hook up headphones and listen through it. It just no longer works without being plugged in. I found batteries for 30 dollars but could not find battery specs on the 4G. I vaguely remember hearing that it was not a battery change but harware changes that created the better battery life. Any help is appreciated thanks.