If you found out the specs of the backlight are you could probably find a florescent bulb inverter to do the trick. Either a huge ballast for overhead lights, or maybe one of those little compact florescent bulbs you get from IKEA that save energy. Sure it’s an extra wall plug, but it may be worth a try if all else fails!

There’s also a good chance that other parts failed along with that MOSFET, so always bear that in mind when buying replacements.