You will have to be very specific with everything... the equipment you are using (router, AP, etc) the settings they are set at, etc.
Because first of all, as was guessed at, your issue might be one of security. The DS and DS light, according to Nintendo, will only work with WEP security. If you are using WPA or higher security on your wireless connection, then you will not be able to connect.
Also, as has been pointed out (kinda), your router and AP must be set to allow for a mixed protocol connection. Your DS uses an older wireless protocol 802.11b. In order for you to be able to connect to an AP or router, the device must be set to allow for a mix of protocols, and not be limited to ONLY a specific protocol like 802.11G or 802.11N.
So, without knowing exactly what devices you are using, and what settings they are at, we can only make random stabs at the issue, and not really solve anything for you.