There are a few different things to consider when a TV is not working properly before concluding it is broken. If the television doesn't turn on, the screen is damaged or the channels or sound don't work, troubleshoot the connections and settings to either fix the problem or determine if you should replace your TV.
Plug in the TV and press the "Power" button. If the TV does not turn on, unplug the TV and plug a different electrical device into the outlet to see if there is power going through the outlet. If the device does not work, plug the TV into a working outlet.
Check the TV for exterior damage, such as a cracked screen, severed wires or broken inputs. Note any recent accidents or trauma the TV has undergone that may have resulted in physical damage. If the TV was dropped, it is possible that exterior damage could have gone unnoticed or become more predominant over time.
Check all the TV's connections to make sure they are tight and properly plugged into the TV. Both audio and visual problems are often a result of loose or improperly connected plugs. If all the wires are plugged in tightly to the right connections, there's a good chance the TV is broken.
Press the "Menu" button on the TV's remote, select "Channels," then check the antenna source and make sure the selection matches the type of antenna you have connected to the TV. Change the antenna source, if needed, and run a channel scan. This takes a couple of minutes. If this doesn't help, call your cable provider to make sure there are no problems with the cable service. This only applies when your TV does not get channel reception.
Press the menu button on the remote and select "Audio." Select "Speakers" and make sure the correct speaker source is selected. Change the audio sources as needed since a TV with the wrong audio source selected does not play sound.