My name is John,
It sound like you have a defective power supply, I have worked on a ton of them and the power supply is a simple switch mode supply that uses a few fets to take the Line voltage of 120 volts @ 60hz AC to a few different DC voltage supplies like 24vdc, 12v, 5v, 3.3v and 15v all DC which is what most electronics run on.
To check for obivious failure,
First remove the back cover, which means laying the set on its face on the floor and removing the stand as on this unit the stand block the cover from being removed. To lay it safely you will need a large area and make sure it is very clean and VERY LEVEL as because this is a LCD even the slightest pressure on the screen itself can cause the LCD to crack so make sure the pressure is only on the front cover around the LCD itself.
You will see a board that the power plug connects to this is called the small power supply. This is your most likely failure look at the board and you should see some cylinders with a silver top they should all be flat if they some are not the board is most likely repairable. The parts will cost you about 20 bucks (when you include shipping and the a servicecenter extra fee most places rob you with) If you do not see any of these swollen caps (the silver tops) then the power supply most be replaced they can be expensive ranging between $100-$250 for the part. First i would open and see if you can save a buck and repair it by replacing the damaged caps. If you dont feel comfortable with replacing the caps this could easily be repaired by a local repair shop for under $150.00 (if they are reputable)
Swollen caps might look something like this:
If you wish to attempt this repair yourself:
read the numbers down the side of the capacitors they should have a white stripe (neg side always install them the same direction) and then they should be marked like this 1000mfd 50v or the "1000mfd" is the micro farad rating this is a contant do not install anything but the same mfd rating but the "50v" is the maxium voltage rating and this you can increase to anything that will fit 65v 100v 200v or larger but never smaller. The bigger the voltage the bigger the size of the cap.
You can order the parts from http://www.digikey.com/ expect to pay around $20.00 for the parts but you will need a good pencil soldering iron, solder and desoldering braid.
If you dont have the tools and materials the cost of the equipment will be more then the cost of having it professionally repaired and when you do it if you make a mistake your ordering a $300 power supply, and it doesnt carry a warranty.
If you have the tools it is simple enough if you dont you can order them from www.mcminone.com
it has to be adjustable and at least 40w
21-3475 - WLC100 Solder Station is the cheapest one i could find that would suit your needs
20-2788 - Solder-Wick Rosin - .110'' x 25' copper wick, this is the only stuff i use there is some really cheap stuff out there and it is horrible to work with in supplies.
21-1840 - 44 Rosin Core Solder - 60/40 - 1 lb. x .031'' - 21 Gauge this is the solder you will need.
Hope this helps,
If you do want to get it professional serviced i would recommend looking at www.citysearch.com or www.tvrepairpros.com
IF YOU HAVE ANY QUESTIONS PLEASE ASK