You should check to see if it qualifies under the 1G Nano recall. If it does, Apple will replace it for you at no cost for a 8 GB 6th Generation silver one.
I did it in november and after receiving the email from Apple confirming the shipping of the new ipod, i still have not received it. Nobody is able to give info wether it has been shipped or not, nor a valid tracking number. My ipod nano 1st gen was still working and it is very weird to find myself without ipod after 7 months. I do not think this is a good customer care. Last time I called the italian assistance callcenter they were joking on me.