iPod not holding charge and sometimes is slow responding

hello my favorite team - i am back to ask another question. i recently sent my ipod to walmart's care plan and they are returning it unfixed as they noticed the screen was replace - how they knew it wasn't professional i don't know.

anyways, i'm pretty sure that i need a new battery since it's not holding a charge - do you think this will fix the rest of my problems. i am thinking it is responding slowly because it doesn't have a good constant charge.

any thoughts and opinions would be greatly appreciated - it's my daughter's old one that i inherited and dang those ipods are addicting and i cant wait to get it up and running properly again....lol