Firstly try holding the power button for 30 second, if that doesn't work then try holding the volume down and power to boot to recovery...
From here either try restarting or a factory data reset, you lose everything but if it works you'll have your Nexus 7 working again.
What happens when you charge it? Does the charge animation appear?
If you do have to return it they'll probably send it off for repair, that's what Argos do with mobile phones if more than a month old and if it's not repairable then they should replace it like for like. So if the 16GB isn't stocked they'll either have to replace it or give a full refund which you could then purchase a 32GB with...
Sent from my 16GB Nexus 4 using Tapatalk 2