Trying to get homebrew running on your PSP? Want to add a screen light to your Game Boy? Trying to figure out how to work your GP2X? By popular demand, discuss it in here! (This forum is for pre-built handhelds, NOT custom made portables!)
I've seen this problem before and every time it has either been a bad LCD or loose ribbons. Just take the Slim apart and look at where the ribbons for the LCD plug into the motherboard. Are they in far and straight?
The fact that it is a screen portion tells us that one of the three miniature LCD controllers on the LCD (there are three that control regions of the screen) has gone bad. This happened to my father's laptop - it is the screen, not the PSP itself. Should be a simple and cheap fix.