It seems it is a DHCP setting issue. It may caused by several reason. First, check if you have MAC filter set up in your router. If you do, add the MAC address of your Wii to your router allow list. If you don't have MAC filter, check your DHCP setting on your router.
Oh, I just saw you are using the dongle. So it is an ICS issue. I have not used ICS for several years, so I kind of forget the details. Look for the default setting for ICS in Windows and punch in the IP address, etc manually in your Wii. Do you have other devices using ICS? Make sure there is no IP address conflict.
I am really confused by your setting. Are you using the dongle on a PC for the Wii to connect wirelessly? Or using wireless router? With a wireless router, you don't need a dongle.