I have a D-Link G604T Wireless Router. My son uses a Wii and wants to connect to the net via the D-Link. I went through the set up which is not hard but at the end I got the 51030 error saying that it could not detect the SSID of my router.
This seemed strange as both my sons PSP's could both see it. When I searched for Wireless Access Points I could see my neighbours but not my own!
To cut a long story short, you need to connect to your router and change the channel to 11 (this worked for me). As soon as I applied the change and rebooted the router the Wii was able to connect to the net.
Hope this posting helps someone else with the same problem.