If you press the power button on your TV and all you hear is a clicking or ticking sound but the television doesn't turn on, that indicates a problem with the power supply. If your TV is under warranty, contact the manufacturer for a repair or replacement.
The power supply on a television transforms the alternating current electricity from your wall outlet into direct current that the components of the TV can use. The power is transformed for voltage, rectified to change from AC to DC, smoothed out and regulated through the use of capacitors so that the internal circuitry of the TV gets a constant flow of DC voltage. The connection between the components of a power supply is made by relay switches that are set to open or close by an electronic signal. When a relay switch is activated, it makes a clicking sound.
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Through an electro-chemical reaction, capacitors store a set amount of electricity before passing it along in the circuit. As each capacitor is charged, it then passes the flow of electricity on down the line to the next capacitor, and the result is a smoother electrical signal for a DC flow instead of the cyclical AC flow from the outlet. However, if a capacitor is damaged or defective, the flow of electricity slows down or stops. Though there may be enough power to switch the relays when the TV's power button is pushed, the flow is stopped at one of the bad capacitors, so the set can't fully turn on. The TV keeps trying to initiate the power by switching the relay.
Unplug your TV from the wall and leave it unplugged for 30 minutes. Reconnect the TV to the power and try to turn it on again. Use a different outlet to power the television and ensure that you have a grounded surge-protector connected to the outlet so that the flow of electricity coming in is safe and consistent. If that doesn't work, contact your television manufacturer for support with your TV. Browse to the website for your TV and find the Support or Technical Support link. You can also find the phone number for your TV manufacturer in your user's guide or online (link in Resources).
If you're very experienced with electronics repair and soldering, you can attempt to replace the bad capacitors on your TV's power supply circuit board. Don't attempt this if your TV is under warranty or if you don't have any experience with soldering small circuits. You could destroy your television and hurt yourself if you make a mistake. Never work on an electrical device that is plugged in. The capacitors on the power supply will noticeably bulge or show leaks if they're bad. The X on the top of the capacitors is designed to split open if too much pressure builds up inside the unit, if you see any discoloration along the lines of the X or bulging at the top of the capacitors, they're bad and need to be replaced. Purchase capacitors that match the specifications of the ones you are going to replace. Note the positive and negative orientation of the capacitors on the circuit board. Desolder the bad capacitors and replace them with new capacitors.