Normally, most TVs will power up after a few seconds of turning on power to allow the PSU to stabilize. When the relays activate, if there is a problem with other powered circuitry, as in an abnormal load, it will then shut down and start the power cycle again. Disconnecting a cable would point to the board that has a problem. However, if that board is connected to another circuit the problem might be in that circuit. This follows Brandon’s find of burned resistors off the main board. Replacing the resistors will not solve the problem until the cause of the burn is found. A schematic will tell you what the resistors power, and of course, if the resistors are burned only a schematic will tell you what the value is.
Otherwise, it is replacing parts till you get results, which can become more costly the a new TV.