Your TV may well have a problem with its power supply - a component heats up and stops working.

When everything's connected it takes 5 seconds and if the load on the power supply is reduced - by disconnecting a board - it takes longer to get to the failure point.

You can buy freezer spray from electronic stores to spray on suspect components to see if it changes things - it helps to know where to spray it though.

Good luck...
May 2015