Since you can see a faint image of the desktop that means the actual video components are good and that something in the backlight system is bad. Since it just went "black" on you the most likely source of the problem is the inverter. Click here and chose the inverter guide for instructions on how to replace it. Going through that guide will also give you an idea if you or someone you know can do the job. The inverter is sold here and a number of other places. Prices vary on them from about $10 USD to $50 USD.
Inverter cables, when they go out normally show there is a problem over a period of time before they fully go out with the backlight flickering or going off/on when the upper clam shell is moved toward or away from the keyboard. The actual backlight/CCFL bulb normally shows problem(s) over a period of time with one or some combination of the following: Dimming, flickering, reddish/orange hue or low level hum coming from the lower bezel area (not the speakers). Though it is rare to find and normally associated with liquid damage, backlight problems can also originate from the control circuitry on the motherboard/logic board. From the details you have given in your question and answers to questions I'd put the chances of the inverter being the problem at 90%+.