It's called Fluorescent ligh bulb.

The problem should be the light bulb (most likely) or the inverter. The light bulb cost about $10 (for 2), the inverter about $30-40. I once replaced the light bulb in my Dell laptop myself. It's not a trivial task. You need to find the manual on disassembling the LCD from your laptop, and most importantly, you need to remember where all the tiny screws go when you place them back. I got 2 screws left after I assembled mine, but the LCD worked ok, so I didn't bother to put them back. I remember I bought my part from Digikey