If I was to go by your title I would say it's inverter board/ cable, but since you also mentioned that the screen progressively died out it could also be the display went dead. I would get the inverter board and cable since they are inexpensive and easy to get and try that first. That failing, replace the display.Here is a link for the Inverter. Here are the Guides for your machine. Good Luck.
A bad inverter board can cause a dead backlight — 2 available at 14.95 each.