Try checking component ic4104. That's the backlight driver and is located in the 11,C quadrant of side A on a TA-085 v1 board. The part number is TB62752BFUG. Test each connected capacitor to ground in continuity mode with a basic multimeter for a short. If one or more of the capacitors are shorted remove those and check the pads where the capacitors were. If there's still a short on both pads where the capacitors were then put back the original ones. Odds are if there's a short to ground but doesn't go away when you remove the capacitors then TB62752BFUG needs to be replaced.[br]
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PSP 2k Schematics (~95% 3k)[br]
https://gamingdoc.org/technical-documentation/handhelds/sony-playstation-portable/official/service-manuals/psp-2000-series-service-manual-1st-edition/[br]
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TB62752BFUG Datasheet[br]
https://www.mouser.com/datasheet/2/408/TB62752BFUG_E_070404-47226.pdf