I can tell you what the problem is with a 6 year old LCD tv.
It will be a few capacitors on the power board section inside of it.
When you get a situation where the power light stays on then goes off after a few seconds it the case.
Depending on how many capacitors you need to replace, will be how much it will cost.
You are not going to be able to work this out till you visually inspect the power board section of the Samsung Lcd Tv though.
I take it you know how to identify when a capacitor is worn out or is not functioning correctly by visual inspection, the tell tale signs to look for that tells you it`s damaged.
In some cases though it`s more than just a few capacitors.
It can be down to the transformers on the board.
Typically on a power board your looking at about one to two transformers.
They are step down, to reduce voltage, where each will step the voltage down to feed another board such as the video input, decoding, and encoding, plus the output signals or frequency's, or a set section of the board if an all in one power and decoder board.
One transformer will also drive the white light, or back light array.
This part is High voltage.
The rest works on about 12v to 25v and above.
If the transformers of the Tv hum, or what we call oscillate then there pretty much done for.
And not worth attempting to fix or replace.
In such a case your better off getting the power board serial no.
Along with the model of Samsung tv, and buying a whole new power board that you will find on e-bay for as little as £20 or a little bit more.