If you want to play Mario Kart DS you should use Wiimmfi since its a revival of Nintendo WFC. Pretendo is a service for Nintendo Network these services aren't the same

Use Wiimmifi, if you wanna play online go to ds internet settings and set dns to 167.235.229.36 and try 2nd if you want 8.8.8.8 or keep it 0.0.0.0