A few things...
1) If your iPod has a click-wheel, it's a 4th Gen. If it has a touch wheel and four individual buttons at the bottom of the display, then it's a 3rd gen.
2) You should probably double-check when you bought the iPod to see if it's eligable for warranty repair. You can do this by going to Apple's support site
- you can enter your serial number and it will tell you if you are still under warranty. If you are, egt it to a retail store or mail it off as soon as you can. It'll cost $30, but you'll get another one if they find that there's somethign wrong.
3 If it's not under warranty, then I'm not quite sure what to tell you. Reformatting and updating the software MAY fix it, but I would definitely get a second opinion on that. I reformatted my iPod once and it was a pain in the ass.
4) You can always put the sucker up on eBay and say you can't get the backlight to work. There's a lot of people (like me) that hardly ever use the backlight, so that's not a major issue to them. Depending on what kind of shape it's in and what generation it is, you might be able to snag anywhere from $150 - $220 for it. It'd certainly go a little ways to the purchase of a new one.
Hope that at least gives you a place to start...