I have SZ480 with LED display (part number LTD133EXBY). And my backlight stopped working all of the sudden. I've ordered a replacement LED LCD from Sony ($400+shipping) since there is no separate inverter to order and was so pissed off when it didn't have backlight as well, I've tested a cable that runs from motherboard to display too and discovered my old screen lits well on the other laptop.
My concern is if there is a switch that turns off backlight when you close the lid that might be broken or any other connector that might be loose that I need to check. What else can I possibly do before sending laptop to sony for repairs.
Need to mention I've upgraded the cooler to the model from SZ7xx two months ago, but since then everything worked just fine and I also have display hinges loose (where they hook up to the display).