How are you? Here's a solution that will most surely work for you.
I have had problems with my nintendo products that were out of warranty before (Nintendo DS, Gamecube, N64) and the thing that ALWAYS solved my problems was to call Nintendo's customer service.
Seriously, this company has one of the best customer services I've ever seen in my whole life. They will listen to you and propose you a solution to repair this.
If they want to make you pay for it, please make sure to insist that it isn't your fault, you went through normal use and you are very very disappointed by this. You used to believe that nintendo products were built solidely and now they break easily.
If they still insist on NOT wanting to replace it to you for free, do the following (I've done it once and it worked).
Write them a real physical letter and send it by mail. Write about how your DS doesn't work properly anymore and how deceived you are with the situation. Tell them that you called the customer service only to find that it would cost you money to get it back on track.
Try this, it'll work, soon enough your ds lite will be fixed!
PS: When my DS broke, I did exactly this and they sent me a letter back asking me to send them the console and they would take care of everything, the shipping costs and the repairs.
Call them today, good luck!