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The flashing red light indicates a fault on the power board inside your TV. This will be due to a faulty component like a capacitor or voltage regulator. Faulty electrolytic capacitors on the power board are the most common cause of this problem. These capacitors will often leak and stop working as the TV set gets older.
If you feel like removing the back off the TV, you can visually check the capacitors on the power board to see if they are bulged or leaking. The power board will be the one connected to the power lead going into the TV. Even if the capacitors appear normal, it is still possible that they have "popped" inside. The capacitors can quite easily be replaced by a TV technician, or by yourself if you have good soldering skills and access to a soldering iron. A TV repair technician will charge around $100 to repair this type of fault on the power board.