If the MS light is blinking constantly, then take the MS out (that fixed my problems with a fake MS). If there is no green light, check the battery (bit obvious, but needs to be said). If there's only a green light, then try recovery mode (holding R when booting). If there are indeed no lights as you say, then it's likely that the battery's at fault, unless you dropped it...
If you've done nothing to brick it, and don't use CFW, then my only idea is if it was dropped. If so, then maybe send it in for warranty fixing?
EDIT: Try with the charger out and with the charger in. Or try getting a friend's PSP and using their memory card and battery. Those are my last troubleshooting ideas, but at least you got plenty to go on.