Tracking down the source of even a simple power supply problem can be a challenge. Start with the most common solutions first, as the odds are those will solve your problem. Troubleshoot the steps on outlet function, circuit load and interference and be willing to consult a professional electrician if a solution can't be found without invasive work in the TV or at any sign of power fluctuations.
Check that the power cord is connected snugly in the back of the TV and snugly into the socket. If you have a cable box, or DVD, VHS or Blu-Ray player or use a power strip or extension cords, make sure all connections are snug. Test the socket you are using with another electrical item to make sure current is flowing. Confirm that the electrical socket the TV is plugged into isn't controlled by a wall switch that may have accidentally been flipped. Inspect the power cord for any nicks or cuts. If the cord itself is damaged and not permanently attached to the TV, a replacement cord can easily be found and ordered online. If it is permanently attached, an electrical repair shop can rewire it for you.
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The best way to identify if the problem is related to the incoming flow of AC power is to connect the TV to an independent power source, such as an Uninterruptible Power Source with the UPS cord removed from the wall socket. If the TV works, you know that the problem does not lie inside the TV.
Make sure the TV is not plugged into an overloaded household circuit. Household appliances such as refrigerators, washers and dryers or even space heaters can induce power drops and increases when they cycle. If you have complicated wiring in your home, multiple areas of the home may be on the same circuit even if they are not near one another, so make sure you know what the real circuit load is.
If power is inconsistent or intermittent creating a flickering on the TV, but not caused from an overloaded circuit discussed above, plug a lamp into the outlet and see if the bulb shows signs of intermittent power fluctuations. If there are fluctuations in power, you should contact a professional electrician because it could be a fire hazard.
Interference is not a common problem but can happen. Of this type of interference, dimmer switches on the circuit shared with the TV may be the culprit by creating power line-conducted interference. You can turn off the power at the circuit breaker and disconnect the dimmers to test this.