The screen turns off after a long period of use

ferraric, You're halfway there! Now all you need to do is find the "THERMALLY INTERMITTANT" and "COLD/FROSTED LOOKING" solder joint on the power supply (switch-mode-power-supply) printed circuit board. Check all the larger and more weighty components first, including power transistors. I'm sure that the web has some pic's of what they look like! The cause of them going BAD is what is known as Thermal cycling! Hot to cold, Hot to cold. You may need a magnifying glass or an inspection microscope to view your printed circuit board! Visit YOUTUBE for disassembly vids and you better have a digital cam to document the teardown BEFORE removing plugs from board-mounted connectors. Good luck! louie12fix or aka 12fix louie