Hello,
Why do you want to sync it to iTunes? If it's for backup, try to copy all files to your computer by using Linux (in a live CD: http://www.ubuntu.com/desktop/get-ubuntu/download ).
Now let's talk about your screen: try to teardown it and check all connectors (link: [guide|600] from step 12).
If you don't want to teardown it (you're afraid to break something), the best solution is to see a qualified technician to solve the problem...
I hope these advice were useful for you...