Hi guys ! Well I searched a bit in the board and found no others guys who have the same problem as me so here is mine.
Ok First I bought a PSP Fat on Ebay and it worked fine. However, few days later, the PSP didn't turn on and didn't charge ! So I started reading tons of tutorials and unmounted it.
The LEDs didn't work too so I thought that it's because of the power fuse . . . I shunted it. But it changed nothing.
Then I saw a video on Youtube where someone said that the problem can be because of the power board and you just need to replace it. That's what I did . . . It changed nothing.
Second, guys you must know:
-The Psp doesn't turn on with the AC adapter or with my PC. Same thing for the LEDs.
-I changed the ribbons too
-I hacked the PSP myself and there was no problem. I also did it countless times before owning the current PSP so I'm sure that I did no mistake in that step.
-I don't think that it's a software's problem . . .
-That PSP has absolutely NO mods

I asked in many forums before coming here and still no one found what's the problem with that PSP.
However I just found a blog this morning here with a pretty interesting solution but I don't know if it really concern me. I'll try contacting that guy.

So . . . Someone here has an idea ?

Edit: I can also add some pictures of the PSP if you want. Just tell me exactly what pictures you want.