The best way is to unplug the wired connection and see if you connect to the Internet. You can also type ipconfig /all at command prompt and see the connections.
Thanks for your answer. It took me awhile but I did decide to unplug the wired connection and discovered that I was still connected. I was then able to disable the wireless and reconnect with the wire.
A simple way of finding out is by going to the command prompt, type "ipconfig" and press enter. Write down the "gateway" addresses for both connections.
Now type "tracert google.com" and press enter. The first ip in the results shows which gateway you are using. Compare it with the gateway addresses of both the wired and the wireless connections and you got your answer!