iPod 1G Nano won't fully charge or turn off

[riotshield]

I've had this unit for about a year and so far it worked fine, until a few days ago. Now the Nano constantly has the charging battery icon, regardless of whether it's plugged in (either USB or AC). Also, I cannot turn it off completely - when I shut it off, it continues to show the charging battery icon. Tried resetting and restoring and neither works. The battery ran down to nothing and when I recharged it the problem doesn't go away. Any thoughts? Besides this problem it seems to work normally. Thanks

 

[siurpeeman]

do you notice a drop in battery life? that is, can you go for the normal duration between charges? if so, i wouldn't worry so much.

 

[riotshield]

Since it won't turn completely off, the battery completely drains within a day or two. Whereas, before I could leave it off for a week and it'd still have juice.