Chosen Solution
I got Samsung UE40D6100 LED-LCD After i bought new remote for my samsung, after couple weeks of using it, my TV shutting down after 30 seconds. I checked everything possible: removed all devices no sleeping mode Update (07/03/2018) I checked all internal cables, no seen damage. I also tried to make factory settings reset (info+menu+mute+power). Still shutting down Maybe i should replace power supply board?
tomisultra since you already checked the settings to make sure it is not in sleep mode etc. you need to let us know if all the power turns off or if the power LED etc. remains on. you want to focus on the hardware. Remove the back of your TV and check all the boards and interconnect cables. for obvious damage. Post some pictures of all of your boards with your question. That way we can see what you see. Use this guide Adding images to an existing question for that. this does sound like either a power supply issue or a main board issue. If it would only be the backlight you would still have audio to your TV.
This can be a power supply problem or even a back light problem. Without seeing the actual set and its internal boards this will be next to impossible to resolve. If you have the ability, open up the set and see whether or not there are any “bulged” capacitors on the power supply board. These provide filtering for the DC power lines and failed ones will allow enough AC through to cause problems like what you are seeing. Update this if you can with any new details.