Hi, well I applaud you for wanting to have a go, but you must make sure that you are starting in the right place, and you have, That is The Power Supply, as, if, that isn't right nothing else can be. But, further, you simply cannot do anything without a Service Manual. The LED's do not tell us what is wrong, This is an old wives tale, I mean what if the fault was with that "Indication" was involved in the fault? Anyway the Service manual, well in this it has everything one needs to repair the set. Now some advice, OK if it is shutting down, after that amount of time, of working and then faulting, then it is most definitely a "Thermal" problem, the way we "Find" problems such as this is "Freeze Spray" you use this on each component that is suspected of being the "Culprit" and you will soon,find that errant component. Now also not every fault is a Capacitor,
I see many, many people that think, that Capacitors are always the "Culprit" now while that may be true in a few cases, a faulty Electrolytic Cap, or ordinary, Cap goes faulty, this is only a SYMPTOM, something has damaged those caps causing them to "Fail". One MUST always find the root "Cause", otherwise if you just treat, the SYMPTOM, the "Cause" will just make the "Symptom" come back, in short order, as the prime cause still, hasn't been fixed., Now Capacitors hate AC ripple, or Over Voltage. Thats it. Oh.. and Heat, if these Capacitors, are too close to a Heat Source, then thats a prime cause of failure. Resistors, hardly ever go faulty,and if they do, it is generally obvious. However it doesn't hurt to check values with our Multimeter. Remember though resistors are made, with up to 20% tolerance from stated value, as such, are not too critical, unless in Timing circuits etc. Always check, the Values, of resistors, as with any other component, with the power OFF. Now Diodes especially "Zener Diode", are another thing to check, those and ordinary "Signal Diode" should always be suspect. next we have Transistors and IC's. The Transistors MUST ALL be checked to see if they have a good, "Junction" this is done, with our meter set to "Diode Test" and usually are about 0.6 to 0.7. With IC's you must check, voltage levels, or Logic Levels, going in and out, have a look at the circuit diagram, and it will tell you what they should be. It is a good idea to always measure the Power Supply voltages, see if a "Rail" is Low, that will be because some component has gone somewhat or all short circuit, to Earth, now, if the "Rail" is Higher, suspect an "Open Circuit" component, like a Diode, or Transistor. The voltages expressed in the manual are spot on, ANY variation MUST be investigated. I have been doing all this for over 30 years now, and I do indeed wish, we could have a set of "Symptoms" and be ables to say.. "Oh that;s the so-in-so and replace this" however unfortunately this although does happen, most "Symptoms" can have literally tens, of "Causes" all often "Interlinked" One simply has to do a methodical troubleshooting procedure, and always think, "are my Voltages Correct" as this is how, you Fix the problem, by making them so. Keep up the good work. If that link above doesn't furnish a Service manual, it is imperative you get one, even if you must pay for it. It will pay for itself in about 2 mins.
The Tools you will need are A SERVICE MANUAL a Good Multimeter, a Signal generator, a Signal Tracer, pref an Oscilloscope, Soldering Iron, De-soldering iron, Probably, too, A SMT Hot Air desolderer (for the Surface Mount IC's) Air, An Anti-Static Wrist Strap, (MOST IMPORTANT, to prevent ESD), Cutters, Screwdrivers, sometimes, Torx, drivers too. Tweezers, are real handy, magnifying glass or eyepiece, a good strong Light. OH and you MUST have the original remote control too, as one needs this to "Program" the Computer in the TV, after, and during servicing, and to be able to put the TV, into "Service Mode" too.
So, thats about it, Also to remember that you are dealing with a unit, that can cause a fire, or an explosion, or both, this is not to be undertaken, lightly, for instance if one services a unit, and for whatever reason say, it caught fire, and burned, say, a house down, and heaven forbid, killed, someone, the REPAIRER of the UNIT is Criminally LIABLE, just a little point to remember, to ensure you ALWAYS DO A PROPER JOB.
it is my professional opinion though that everyone should take their units to their manufacturers approved service center, contacting a head office, of your unit & getting an approved service center is just SO important, even worth the extra to ship it, you see, at those places, the Engineers, are trained on the equipment you have, they usually have parts on hand, and do the job quicker. Anyway do that and get a "Quote". This way, at least, you'll know weather to repair or replace.
http://www.mediafire.com/?69ky1jqemn0
service manual, this is NOT the exact model it is just so you get an idea. The only ones I could find were pay for manual.
http://www.manualnguide.com/download/manual-guide/samsung-la40r81bd-lcd-tv-user-manual.html
user manual.