If there is still a picture on the screen and it's really, really dark your backlights went out, no question. The way to fix that would depend on what exactly the problem is; it could be the power converter - the bulbs are a different voltage than the screen - or it could be the bulbs went out. Either way chances of fixing it are slim to nill unless you have some soldering and electrical testing equipment, lots of time, and a bit of luck that you can find a replacement part for whatever went out.
In short, yeah, buying a new one was a good move.
Edit: oh doublechecking your post, sounds like it was definitely something in the power system that went out. Don't pitch the thing out the window though, it's not as toxic as a CRT but it's still toxic, those bulbs are florescent :P Also a bored geek with above mentioned equipment would probably appreciate a donation.