From my understanding - Argos are responsible for this faulty product. They sold you the product, which had a guarantee for 2 years - it's up to them to follow up with their supplier on this, not you. Repair, Replace, Refund is what they should be offering you. Do NOT accept their reasoning of 1 year only.
Document all your dealings with them, get full names of who you talked to, dates & details of what was discussed. Ask to speak to a supervisor to try to resolve it, get their name etc & write it down in front of them. If no satisfaction there, then put it in writing with full details (some letter templates on the consumer web site) & send it in to Argos. Don't get aggressive when dealing with them, be confident, polite but firm and don't back down. Don't feel embarrassed if people are listening when you are discussing this in the shop - you are well within your rights on this.
Good luck with it...