How do I determine if disk or battery are bad?

Need help in determining what to replace on my ipod. Am thinking is either battery or hard drive. When I turn it gives a dim Apple logo then after 5 seconds goes to the 'Connect to your computer. Use ITunes to restore'. Displays that for 15 seconds then turns off. Same occurs when I try to reset. I can hear it hum a bit when turned on - am not sure if the disk is spinning. If the battery is bad - I thought the IPOD would work when plugged in and it does not. I think the disk is bad. Want to get some thoughts on where to start. When connected to my computer is not seen as a disk device by the OS and can not be restored.