I had problems getting White 2 online (even though my 3DS could get online perfectly) and finally fixed it by setting up a static IP address. You may have to also change some settings on your router to prevent it from auto-assigning your 3DS an IP.
This is your answer.. I had the same prob with the original Pokemon White. You have to go in and manually assign your IP by looking it up on that page metriodfood gave you.
Which I did. I've been trying to figure out the make of the router but I can't seem to find it on the webpage, nor can I find it anywhere on the actual model.
It's one of those BT own brand modems. BT Home Hub 3.0 I believe.