There is an easy way to check if a remote is working or not. Put new batteries and locate the small LED on its head. Its a small white diode but emits Infrared which humans cannot see.
Notice the two wires inside the 'bulb' are of different
Now look at the LED through a digital camera of a mobile phone. The idea is that the camera sensor can 'see' the LED glow when a button is pressed and will show it glowing when you press any key on it. If it is not lighting up then probably the remote is faulty.
You can replace the IR diode yourself if you have soldering equipment and some skill. Purchase a new one at any electronics repair store where you can buy soldering equipment and solder it where the old one is. Be careful as the diode is polarized meaning you must solder the new one EXACTLY keeping in mind the shape of the filament.
There may be other faults also like disconnected leads or the pad dirty making key contact difficult. In worst case the IC inside may be damaged and it is not worth repair.
If you find the remote OK (the camera test is +ve) then its likely the problem is in the TV. There is a small sensor on the front to receive the signals from the remote and may become faulty.
And if you need to buy a new remote it is better to buy the original or a replacement (if original is unavailabl). There are 'universal' remotes also that claim to control most of the equipment in your house but please keep in mind that they may not work with
your TV leaving you with a good useless remote and some waste cash.