Having the same issue as bveals on my nephew psp 3000.
I assumed it was the LCD so I went and so I got a replacement on ebay and after a install and some playing around on his spiderman game the screen went blank. I have to hibernate and then restart his psp for the screen to come back.
If it was a lose backlight fuse where on the PCB is it so I can add some solder hopefully that might fix the loose problem or might need to replace it as lobo had said.