This sounds like a problem with your power supply circuit board.
Often times poor quality components are used in the LCD TVs and they tend to cause the televisions to fail prematurely.
Bad electrolytic capacitors are the most common cause of power supply failures in LCD TVs.
You can sometimes visually identify a failed capacitor by its BULGING TOP or by the scorched gunk leaking from it.
If the unit is still under warranty, you should return it immediately to the place of purchase for exchange or refund.
If the warranty has already expired you will have to decide on a course of action. You can just buy a new TV, you can pay someone to fix it for you, or you carry out your own troubleshooting and then buy the replacement parts and install them yourself.
You have to weigh the unknown potential cost of repair against the known price of a brand new tv.
And don't forget the new tv comes with a warranty while the repaired one, in questionable condition already, just keeps getting older.
If the problem is in fact just the power supply circuit board, a television technician will probably charge you about $150 to fix it. But if that's not the only problem then there may be additional costs totalling hundreds of dollars.
Trying to repair your own LCD TV can be financially risky, you can end up spending a lot of money changing out circuit boards and still end up with an unreliable or even dead unit in the end. It also requires at least a little bit of skill, know-how and common sense in order to avoid damaging the unit further and to keep yourself safe while working on the electronic parts.
Let me know if you are willing to disassemble the unit yourself and conduct some testing and troubleshooting and I will help guide you through it with much greater detail.
Here is a link to another senior expert's response to a similar question and his excellent LCD Troubleshooting Guide:
http://www.fixya.com/support/t8133519-not_power_up
Please give BUDMRTN a thumbs up too on his page if you find his advice helpful at all.
Please comment back here to this page if you have any questions or require further general assistance and I will respond as soon as I see it.
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Good luck and thank you very much.
Joe.