It would probably be cheaper to do it yourself, but just be aware that you need patience to deal with the process. Buying another DS lite should be a last resort, in my opinion.
One Thing I did, was increase my warranty on my DS lite in ClubNintendo, and that lowers the price of repair. It cost me 50 dollars to get my DS lite all fixed up. If you don't increase your warranty through clubnintendo, its gonna cost even more.
All you do is Join Club Nintendo, and type in the serial number on the back of your DS lite, and BAM! your warranty is extended, absolutely free. Make sure you e-mail or phone them about specifications before you send it Nintendo though, because I didn't need a Battery replacement.