Ipod wont hold a charge

I just got a brand new Ipod 2gb nano second gen. it seemed as though everything was working fine when i plugged it into my computer to charge, it synced with my computer quite well and everything was going good until after charging it for a night i unplugged it from the computer and it just dies like there is 0 charge in it, and i have repeated it tried charging it. it will charge up to the point where the screen shows that its fully charged, then i unplugged it and it dies, then once i plug it in again, it shows the apple icon screen then acts like it has no charge.
i've tried resetting it but nothing has worked so far