It's probably not that hard, I've only done one Sony that I can remember and it was easy enough as long as you're okay with laptops in general. It's the price thing, though.
But you should be able to google directions. I'd reseat the screen and ribon connection if at all possible, it's not unheard of for them to become a little loose and that can cause issues like this. You can google instructions usually, I don't think Sony carries service manuals for stuff like this.
Check out this site for instructions and replacement information: Laptop LCD Screen
They have a lot of pics and videos for replacing many screen types. They can sell youa screen, too, but you're probaly better off finding the model # and locating it on ebay, that's usually cheaper. They'll do the labor for a price if you ship it in.