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A Broken iPod
New Battery
Soldering Iron
a note on batteries, you can get them off of ebay, but i got mine from iFixit.com.
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Apple has been doing a recall on 1st gen ipods since 2005 and its still in effect today (july 2012)
You can get it replaced with a 6th gen nano (with the touch screen & radio)
Of course, its your choice. But if you replace the battery before sending it in they might send it back saying its fine.