You have to check the remote control first, for its infrared emission, before confirming the infrared sensor inside the TV is defective. The LED you see lights up, when you push any button, is not a symptom of proper emission of infrared rays. Infrared rays comes from and infrared LED, fitted at the front end of the TV, and these rays are invisible to us. But you can check it, with a cellphone with camera option. If you wish to know more about how to check and repair a remote control, check the sites linked here.
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