If the PC's not picking it up on USB, definitely try it in a mains charger. As mentioned above, I've often found that USB charging, esp from cheap in car chargers, isn't quite enough to get round the initial charge, start up, screen on, discharge cycle.
An over night charge would be the next bet.
Edit – if the above doesn't work and you bought from Amazon I'm sure they'd replace it without hesitation – their returns policy is legendary 🙂