A white screen on a Nintendo DS (often called "White Screen of Death") is a common hardware fault. It usually means the system boots but the display isn't receiving data. Here's how to diagnose and potentially fix it.
Warning: Opening the DS requires patience and the right tools. Forcing components or stripping screws causes permanent damage. If you're uncomfortable, seek a professional repair service (Console5, RetroFixes, or a local retro shop).
Most white-screen issues are a loose or damaged top-screen ribbon. Reseating it fixes a large percentage of cases.