Could be one of 2 things.
1. Defective LCD - Get a replacement.
2. More likely - Blown Backlight fuse.
http://www.mr-vizitkin.ru/images/stories/psp_fuse.jpg
Thats a link showing all the fuses on the psp go - i can elimiate the one on the right as that is the sound fuse. I dont speak russian but i have been informed from this site that the backlight fuse is marked F and is on the left.
Credit to http://www.ifixit.com/User/283651/chiwu12 for the russian piccy and the fuse label