tofu

i think you should file to bbb now, because it takes a long time to process.  
visa won't deal with it, because you did authorize the transaction and the amount.  unless you told them they charged you a different amount that you auth.
i heard a similar situation recently,  someone brought a tv with free installation.  when he returned the tv, the shop charged him the installation free.  the store manager explained to him, it is free if you buy the tv, but you don't buy(return) the tv, so it is not free anymore.  just like gift with purchase, if you don't keep the purchase, you need to return the gift as well.  i am not sure how's this end.   but be honest, they did state clear in the refund policy.
shutterbug is right, "the product does not work as advertised" is the good point to get your money back.
其實佢明明將 shipping fee 加咗落去果 item價錢度， 又懶係俾著數人地話 free shipping, 究竟佢咁做有咩好處同合唔合法嘅哩.  easy for book keeping + some manufacture may have control of the price, so in this case, they are not lower the price, they just give bonus.  they have  discount with usps, so the amount they actually paid is much less.  this is free shipping with purchase, not adding shipping fee to the item.