I can fix it, i know I'm a guppy but I fixed a similar issue on my PSP like 2 days ago. And I'm gonna mod it later. I won't charge you anything except if something needs replacing. It does sound like your back light fuse is blown and that takes like 10 mins to fix. And I have my PSP to test which part is
. Lets hope for your sake everything is sweet and that its just the back light.
LaZeRaY
EDIT: Changed the our sake to your sake