Ipod shuffle 3rd generation

Hi

I'm facing big issue with my Ipod shuffle 3rd gen , The battery died and went to Apple Authorized service center to fix it and but the answer was sorry we don't have spear part battery for this shuffle and no replacement for it since this products already withdrawn from the market and no stock !!!! so this means thow out your Ipod shuffle !!!!! waste of money again .

Now i need the communities help to fix this issue out of Apple authorized center , Is there any way to find a battery replacement for this shuffle and what the cost for original one .

The other issue that when I'm connecting my shuffle to my notebook The ITune or the Windows 7 Not showing me that it recognize this shuffle look like nothing connected .

Please let me to retrieve my music from this shuffle because i don't have a backup for it .

Regards