iPod touch 3g can only use with wall charger.

hi guys i have an ipod touch 3rd gen and i can only turn on when i connect to the wall charger and if i disconnect its turn off and the other thing that he make is that when im using whit the wall charger appears the button that say slide to power off or if he dont say this he make like i put to sleep and the i need to hit the home button to slide to unlock and he does alot of time so i think that the battery is bad and i dont know if the power or sleep button is bad soy can help me please? thanks...