There are two possible problems with the PSP.
The first is that the connection between the wire connecting the screen and the mother board has become loose. Vertical lines are often signs that the screen is not receiving all the data required to fill every line.
More likely, the lines on the screen were severely damaged from the drop, rendering them inactive. This means that you will require a new screen.
Because of the purchase date, your product is still under Sony's initial warranty. This means you can request a repair or a new device. I have included a link to the "Service Request Page" to speed things along for you. Note that there is a $50 fee for replacing and diagnosing a problem with a device. While it may seem costly, due to the early age of the device, it may be best to go through Sony as not to void the warranty.
Sony Support Page
https://service1.us.playstation.com/rma.htm?_flowExecutionKey=_c82CAAC8E-A2F1-D305-5FA5-9DB224B922D9_k54341030-70C9-01DA-D990-B296489121F3
Hey I have the same problem except mine actually hit right on the corner of something. I think if you e-mail sony they con send you new parts to fix it yourself. Otherwise you can send it back to sony to either repair or replace it.
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