First and foremost, what’s the brother said he wants you to do?
I think to my mind he’s not that bothered about it, if he can afford to spend £1100 quid on a TV and then leave it at what is ostensibly someone else’s house for four years.
Plus I’m not seeing how it’s your fault particularly, you’ve not damaged it or broken it, his TV has happened to develop a fault whilst at your house. If I rode to your house and my chain snapped on your driveway, would you be liable?
Whether or not you’d want to give him some money would ultimately depend on what he wants, what you want and the nature of the relationship with your brother. If roles were reversed, would you expect him to pay up? But I’d feel that anything you offered would be out of goodwill, not obligation.