First, the toy is 3 years old. The fact that she took care of it for this long without issue is a good thing. It does mean that she places a value on the game.
Second, things break. THat's the way it is - sometimes it's an accident, sometimes not. But it sounds like you'd rather accuse her of lying than getting to the bottom of the issue in finding out what happened.
Also - note that there's a distinction between lying and misrepresenting the truth. You asked her where it was, she said it was fine (meaning it's not stolen or lost). You didn't ask if it was broken. She may have misrepresented the truth, but she didn't lie. (And yes, you need to have a conversation with her about that and she needs to know that ommitting information is equally as bad as lying.)
She already knows it was very important to you that she take care of it (and did a good job of it for nearly 3 years). She already knows that it's expensive because you've told her so. (No wonder she didn't want to tell you what happened.)
Talk to her. Let her know that you found it, turned it on, and there was an issue with the screen, and you'd like to know what happened. Try to actually listen to her, and not condemn and criticize her before you find out what happened. Once you find out what happened, then you can try to figure out how to proceed - whether to get another DS or not, and whether or not she should contribute to the new DS, and what that would mean (doing chores, etc., and she should be cleaning her own room). Find some sort of "merit system" (since she's too young to really have a job) and then once she's "worked it off", then get a new system.
You could really turn this into a teaching tool/life lesson if you approach it right.
Just a few thoughts....for what it's worth...and good luck!