My guess would be that the ribbon cable for the LCD finally gave it up. I've never had to work on one of these, but I did work professionally for a cell phone refurbisher for a few years and saw this exact issue with all of the models of "slider" phones that would come through. It wasn't always the issue, but it was incredibly common and normally just required a simple ribbon swap to get it going again. Chances are, if your PSP has seen more than occasional use over the years, that's exactly what you're looking at.
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Need Stadium Events + Panesian titles, 6-in-1's, Menace Beach, Moon Ranger & Secret Scout to complete my licensed/unlicensed sets.
If you've got any of the above for sale, hit me up!