How long have you had the set for?
Additionally, are you saying that currently the set shows no signs of life at all?
What you've been doing when unplugging the set is known as a hard reset and it effectively drains the residual current from the power supply. This is usually a temporary fix for a problem in the power supply itself.
The most common cause of this problem in these sets, is failing capacitors in the power supply. They are similar to batteries, in that once they are charged, they can continue to run inedifinitely, but once they receive several surges, the resistance gets so low, that they act as a short, and can intermittently shut down. The solution is to have the capacitors replaced. Average cost for this type of repair is around $200 parts and labor.
You can use the link below to locate a service center in your area:
If you need further assistance, let me know.
The first thing you would want to check for in the set, are the capacitors visually, making sure none are bulged, swollen or leaking fluid. The Power Supply is the board inside the TV that power cord directly attaches to. The picture at the link shows a leaking capacitor:
http://www.google.com/imgres?imgurl=http://www.mikerepairscomputers.com/blog/wp-content/uploads/2009/07/Bad_Capacitor_01.jpg&imgrefurl=http://www.mike repairscomputer s.com/blog/hardware/bad-capacitors-your-computer/&h=600&w=800&sz=114&tbnid=JA6P6E-fpa5A1M:&tbnh=90&tbnw=120&prev=/search%3Fq%3Dfaulty%2Bcapacitors%26tbm%3Disch%26tbo%3Du&zoom=1&q=faulty+capacitors&docid=Jfij2k-0Zi2uuM&hl=en&sa=X&ei=PS67TrjyHa_KsQKfh4m8CA&ved=0CEIQ9QEwAg
Any that do not appear cylindrical, or are leaking you would take the rating (In uf), and the voltage off the cap (example: 2200 uf, 50 vdc), and cross reference them at the sites below:
They each solder into place with two leads, a positive and a negative. Make sure you solder the news ones in the same way, or they will explode when the TV is powered up.
If you do not see any signs of failing caps, then it would be much easier and more cost effective to simply replace the Power Supply Board, which is a plug an dplay module and can be purchased at the link below: