I say try and see if logitec has the same deal and try that! Seems legit because obviously the 'protector' didnt 'protect' your device in the first place and they should fix it or you could sue for false advertisement!!
ok hopefully this hasnt been said:
Usually on products that are suppose to protect an expenxive produce (logitech playgear) then it should fall under the products warrenty (protector) that if the "protector" doesnt do its job/damages your psp, you can send in you expensive item, in this case psp, to get a new one. I read that on some peliclen protector thing.