Even though I have a wireless router, I tried to connect my Wii to it and it wouldn't let me (coz had a computer friend help us connect our PC's to the new router..and dunno what kind of security it has)

For the time being..I want to be able to connect my Wii not wirelessly with existing cables at home. Is it possible for me to connect my Wii through a PC with internet already working? (Without having to buy a Nintendo Wi-Fi thing)