i had a similar incident happen to me back in march. I must of had a faulty recharger because one day when i plugged it in, i saw sparks fly outve the psp where you plug it in and it wouldnt turn on. My first thought was that it fried my battery. After that i thought that my recharger broke which happened to be the case. It seems that when it happened, it zapped all the energy outve the battery.
What i did was just let me psp sit there over night. what happened was that i turned it on the following day and it worked so i tried to recharge it but with no luck. So before my battery died since it had like 3 mins of life, i recharged it by plugging it into the computer via usb till i bought a new charger.
You should see if your charger works at all since thats whats probably broken. If the light turns on on the psp, then its working, if not then its probably broken (assuming your psp is not broken)
Your battery might be completely dead so it wont turn on. I suggest that if you can get your hands on another battery or charger do that and see what happens.
If both of those cases exist, then unless you can try on a different psp, assume that your psp is broken. This would most likely be beyond repair unless done by someone who knows what they are doing.
Chances are though that its your charger or battery but i cant tell for certain without details.