My psp is turning on but it has a blank screen.

It is odd that if you caught it it would still not turn on. Perhaps something inside just disconnected. If you are technical you may want to open it up and check to make sure all the connections are hooked up.

Always start with the simplest answer first so make sure it is charged and the headphone socket is not damaged.
Take out the battery, memory card, headphones and disk and then hold the power switch on (up) for 30 seconds.
Next reinsert the battery and try it again, if it works at this point switch off, clean the contacts on your memory stick duo, reinsert it and switch back on.
Lastly clean the laser in your UMD drive, you can do this with an alcohol free CD wipe wrapped around a cotton bud (q-tip) and try it with a disk.
If non of this helps post back.

does it turn on turn up the volume does it make noise of scrolling toolbar if you can hear it backlight is gone buy a back light from a place that does refunds and put it in and try it if still black fuse might be gone folloow this tutorial how to do it if you are technical enough to do it

http://www.llamma.com/PSP/repair/PSP_fus...