Chosen Solution
The backlight to this Samsung UN40ES6100F LED TV is blinking. I can confirm there’s a picture onscreen because when plugged in, the backlight flashes on and off randomly, often with a second or two in between flashes, though the pattern is irregular. On the inside, I can’t see any bulged or burnt capacitors on the analog board. My particular model has three boards attached, and a visual inspection yields nothing awry.
Pictured: Analog Board
Pictured: Picture shown when aiming flashlight at screen
The symptoms would certainly lead me to suspect bad caps. The fact that an electrolytic capacitor looks good is no guarantee that it is good. They’re cheap enough - just replace them all, preferably with ones with the next higher voltage and temperature ratings. (Make sure you solder the replacements the right way round.) Meanwhile you might like to invest in one of those cheap Chinese bare board ESR testers you can get on eBay and test the ones you take out, just as an exercise.