Bwaaahahahaa, that's tickled me - your Wii's MAC address has nothing to do with Apple Macintosh computers.......... MAC stands for Media Access Control and it's a unique number assigned to the wireless network adaptor in your Wii.
On your router, if you didn't want to set up WEP or WPA security, you can still secure access to your router by allowing connections to it based on "allowed" MAC addresses. You should have an option called "MAC address filtering" - if you turn this on and enter the MAC address of the Wii, your laptop, any other wireless device that needs connectivity in your home then only these devices can use your router.
What router do you have? If you like I'll help you get connected again.