Your problem is: The Inverter (connects the power to the bulb) is dying.
Your solution is: Open up you LCD panel and change the inverter.
Continue with this instructable to fix your screen.
Step 1: Open Up the LCD Screen
Step 2: Underneath the Plastic Panel
Detect where yours is.
Step 3: Remove the Inverter
Take of the power connectors from the inverter, unscrew the inverter from the metal panel and place it in a safety Ziploc bag.
Caution: The inverter has literally thousands of volts inside it - and if you touch the wrong part you are toast!
The rest of the instructable will come when my NEW inverters arrive to my house...Good luck!