firstly, how is your router configured? is it assigning IP addresses (via DHCP)?
if not, enable the DHCP service.
secondly, are you implementing security measures (which you should be!!) such as MAC address filtering / WPA encryption?
some routers require that you enter the MAC address of the hardware that you wish to connect to it.
on the Wii, go into the Wii Options section, browse for console information and make a note of your (wireless) MAC address, it will be in hexadecimal format e.g. A1:B2:C34:E5:F6
using your pc, go into the router configuration pages and check if the router is either ignoring MAC filtering, or if Filtering / Access is enabled, enter the MAC address of the Wii into the permitted list.
if you have encryption enabled (either WPA or WEP) make a note of your encryption key and enter this into the wireless options on the Wii.
if this fails, move the Wii nearer to the router to see if it's a signal issue.