Originally Posted by OhSnapWord
Is it a desktop PC? If so, you can assign your PC a static IP address that is outside the dynamic range.
Usually routers have a range of IP addresses that they assign to clients. You can also increase that range if you have a lot of devices on your network.
Considering most devices have a range of 100 addresses in their DHCP queue, I'd say it is unlikely the OP will have to expand the dynamic range.
However, I agree with the statement that the OP should try issuing static IP addresses.
In Windows, you will want to select Internet Properties, select the wireless interface, and hit Configure. Then you would want to tell it to use a specific IP address; as mentioned, you want to use an address that is outside the range issued by the router's DHCP server.
Many routers use the range 192.168.0.100-200, so using a low number like 192.168.0.25 would work.
Keep in mind that unless you have some form of Quality of Service turned on, the Wii may be hogging all the bandwidth. I have the same problem in my home.