Re-reading the service manual for its diagnostic tree and testing. The only place I've found that manual is at samsungparts.com. Remember this isn't a TV repair forum so I'll share where I find things.
TV: I have a Samsung HLT6187SAX 61-Inch Slim LED Engine 1080p DLP. No bulbs, no color wheel. Three LEDs create the picture. Owned since 2008. Three small lights on front....standby, timer, and led. When TV off, the standby light is on, when TV on, led light blinks 2 or 3 times, then TV fires up. That's the normal operation.
Past Work: I have replaced the DLP chip for the white dot syndrome in the past and I have just replaced the 5 capacitors in the power assembly as those are the two most common issues. Others have said the red LEDs are also finicky but there is no way to tell except to say, at no time does the picture come up without the reds.
Issue: When turning TV on, sound comes on but picture does random things. (1) Sometimes no picture, (2) sometimes picture comes on for 3 seconds to 15 minutes....then goes dark, (3) sometimes pink screen with old fashioned looking TV noise flipping up over and over, (4) sometimes picture shows with a strobe light type effect of going from green screen, red screen, blue screen, etc. Eventually after 15-20 tries, picture comes on and stays on. When standing close to the TV while starting it, you can hear the fan come on and hear the TV trying to fire up electronically 3 times in sequence with the little LED light on the front of the TV. Any ideas?