Depending on where you live and where you bought the product, there may be what is known as an implied warranty that the product must be of merchantable quality or fit for purpose.
I know where I am there are consumer protection laws which means that if you sell someone an item which does not work, regarless of your company policy, you must give the customer a refund or offer to replace the product with one that does work.
Check this info
http://en.wikipedia.org/wiki/Implied_warranty
But don't accept this as legal advice. Regardless if you talk it up in store the spotty teenager behind the counter and his manager are likely to give up if you sound like you know what you are talking about.
I write and negotiate contracts for a living and these sorts of things are common practise in many jurisdictions particularly in the US and Australia.