if it's the same problem as my sons and his cousins PSP screens then you don't fix it, you replace it. go onto ebay and search for replacement psp screens. i've bought and replaced both broken screens with 100% success. it's really fiddly and you'll need some small cross head screwdivers and lots of patience but it's very satisfying when you turn it back on and it works. the company i got them from via ebay were based in Hong Kong and, interestingly, the screens were made by Sharp and not Sony. They weren't very pricy either. about £15-£20 delivered 5 days after ordering. Good luck.
Copy the link below into your browser and have a look.
http://shop.ebay.co.uk/items/_W0QQ_nkwZreplacementQ20pspQ20screenQQ_armrsZ1QQ_fromZR40QQ_mdoZ
marsbarfingers, March 2009