It could be an issue with the power supply, or a different circuit board inside of the television. Without inspecting it, it's difficult to determine. I'd recommend having a technician inspect your unit.
My LN-T4069F LCD TV is taking longer and longer to turn on. I can hear what sonds to be a relay that clicks every few seconds to retry. Eventually it will start indicating by the glow at the bottom of the screen that it's going to turn on. Could this be dust in the high voltage backlight section? The high voltage PS? Or the Backlight lamp? Can I fix it?