If the unit stopped working less than a month after you bought it, then the shop would be obliged to replace the item or give you a refund. However, if there was evidence that it may have been subjected to accidental or deliberate damage, then i doubt you would get it replaced or repaired under warranty.
As for the form you signed, this is a mystery to me, why would you sign a document to say you were responsible for it not working if you wasn't.
You are entitled to receive a copy of any document you sign, or how do you know that it wasn't altered after you signed it.
If Argos refuse to replace, repair or refund on this item, I suggest you go to trading standards and tell them everything you've said on here.