A window has come up telling me that another computer has the same IP address as mine. Would this be my Wii that i am using Netflix on?
More than likely - I got one of those the other day, and I've got my x-box, and kindle all attached to mine.
It is the Wii that you are using Netflix on, which is making the the Window pop-up appear. In order to get rid of the pop-up message, you should shut off your Wii so that your IP address can be configured to one network.