Why do you don't try to put a secure key?
Only configure a WEB connection, as the newest one, is not capable by the DS.
Then erase all your connection configurations and try again. Go on and search for an access point and then you know what to do.
If the problem persists, then try to connect other device such a Wii or other DS (or just a computer with wireless)
If you get the same problem on all the devices, try to configure your router, I can help if you don't know. If all the devices but your DS work properly... I'm afraid that you will need to call to nintendo for a replacement...
Also... put your connection secured... your neighbors must be happy if they know that there are free wireless haha