Common Faults With The DS, that are relatively easy to fault find and fix
1) Green light comes on for a few seconds, one screen will flash - DS turns off = This is usually a faulty screen, the screen that flashes is OK, the other one is faulty, replace screen and all should be OK (If you have a DS Phat and the top screen appears faulty it can be the ribbon cable, with a Lite the screen and ribbon are one unit, with a Phat they are seperate)
2) Unit wont charge = Blown fuse 1 on the board, very small surface mount fuse next to the power socket on the board
3) Unit dead, nothing happens = blown fuse 2 on the board, located next to the DS game slot
4) Green light comes on and stays on nothing else comes on = faulty WiFi unit, replace this and retest.
5) Touch screen either does not work, registers in a different place, or part of the screen does not register at all = faulty touch screen.
These are the usual suspects, however if this does not fix it then the unit is probably beyond easy repair, for parts I usually get them from dealextreme.com as the postage is free and the prices are cheap, however be prepared for a long wait usually 3-4 weeks!!