https://help.argos.co.uk/help/refun...port-and-repairs/returnsproductsupportrepairs
Argos say, if it is faulty and still in the warranty then they will sort a repair or exchange or refund.
If you have to go back to the shop, print this out or show it to them on the phone. If they refuse to honour it ask them if they can give you a written statement refusing to do so so you can pass it along to your solicitor, hopefully that threat will get them moving.
If they refuse, then take it to an independent person and have them document the faults and the repair and then put in a small claims court claim.
I recently got into a spat with the DVLA, who claimed that because I didn’t tell them quickly enough that my new licence got lost on the post I had to pay for a new one. After several emails of them being outrageous i lodge a claim, they resisted it right until the last minute, but once it got scheduled they suddenly changed their mind gave me back my £20 and paid the £35 court cost. I have framed the settlement agreement and keep it as a reminder that it doesn’t matter how big and nasty you are, when you are wrong you are wrong and I won’t let you get away with it.