Brand New iPod Nano 6G does not hold any charge out of the box

I have just purchased a brand new sealed iPod Nano 6G from a friend. Everything works perfectly when the charger is plugged in but after a few hours of charging, the iPod just shutdown when unplugged. iTunes recognises it and I've synced all my songs to it. I suspect that the battery died because the iPod sat inside the box for too long (probably more than 1 year because the model has been discontinued quite some time).

I have tried to check for the warranty online and I am asked to indicate the date of purchase. So do I input the day when I bought from my friend or the day I unboxed it? Do I need any proof of purchase to prove this because I don't have any. And is it likely that the warranty is still in effect?

Thank you