You are going to want to check to make sure that your connections are securely in place on your LCD screen. Dead lines and stuff is indicative of a failing screen, but that coupled with the fact that it is randomly blacking out completely is more indicative of a bad connection, not a bad screen.

Here are guides on how to open a PSP fat and PSP slim. Hope they help, although I would suggest being COMPLETELY CERTAIN you know what you are doing before you go opening up your PSP.

PSP Fat: OurHappyShopping Blog » How to Replace your PSP 1000 Screen

PSP Slim: PSP Slim LCD Screen Replacement Tutorial



Hope this helps :D