Unfortunately, the Mainboard, or the Power Supply output to the Mainboard on your set has failed. They work in tandem to allow the set to turn on, the Power Supply provides the voltages to various circuits in the TV, and the Mainboard contains much of the communication required for the Power Supply to turn on.
The power supply is the board that the AC cord connects to inside the TV. Often times, one or more capacitors on this board fail, and will give you these symptoms.
The Mainboard is the board directly mounted to the rear panel of the set, that routes and processes all of the AV signals to the TV. This is a common mode of failure for these sets. Average cost or this type of repair is around $350 parts and labor. There is no reset or series of buttons you can press to fix this problem, and the set will require service. I would personally consider carefully whether or not to put that kind of money into this set, as a new TV can be had for around the same cost as repairing this one.
However, if you'd like you can use the link below to locate a tech in your area:
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