Ipod Classic 5th generation works ONLY when connected

I have an ipod 80GB 5th generation for 5 years now and when I remove it from the charge it stops working instantly saying something like "no power please connect" but for that fraction of second I see that the battery is full in the corner... Someone understand the problem? I guess if the battery was starting to fail me it would have been gradual, because some days ago it still worked for hours without connecting it.

Thanks in advance

Samuel