the same thing happend to my psp 2 days ago. its a short on the mother board. i couldnt find where the short was so i had to fix an old mobo. your
out of luck bro. you need a new mobo...or try finding where the short is and fix it. but what i can tell you is that it is NOT the blacklight fuse or the power fuse. i couldnt find where it was.
a test you can do is to take your lcd screen out and turn it on. if it turns on and stays on then its a power problem ( no brick). it cant power the mobo and the lcd screen at the same time. i tested my psp for like 2 hours and this is all i got out of it. buttttt...... mine would turn on when it was charging.
hope this helps. you might need a new motherboard (mobo). i did