Your right to a refund, in respective of faulty goods, only lasts up until the point where you've legally 'accepted' them. This period isn't defined in law. Under certain circumstances this period might be several months. (e.g. someone who buys a car in November might not discover that the air-conditioning is faulty until the following spring). In most cases, however, the period only lasts a day or so. (i.e. the 'pre-acceptance period' just gives the purchaser sufficient time to take the goods home and check that everything is working. If it is, the purchaser is then deemed to have 'accepted' the goods).
Once an item has been 'accepted', the retailer is then only obliged to repair or replace it (but not to provide a refund) if a problem occurs (due to an inherent fault) within 6 years. An 'inherent fault' is defined as something which was wrong with the item at the time of purchase (e.g. the use of poor quality components or poor standards of workmanship). For the first 6 months there is an automatic assumption (unless there's clear evidence to the contrary) that any problem which occurs must be due to an inherent fault. Thereafter it's up to the purchaser to show (based upon the balance of probabilities) that an inherent fault is the most likely cause of the problem.
So you're certainly not entitled to a refund. Argos have accepted that the problem is due to an inherent fault, so they're obliged to repair or replace the TV. You have the right to state which of these two actions you'd prefer but Argos also have the right to reject that choice (and substitute the alternative) on the grounds of economic viability.
Chris