Freeview (which comes via a normal TV aerial) and FreeSat (which is what you get through your satellite dish) are completely different services. The signals are on different frequencies and transmitted in different formats. Consequently, they need different devices to decode the signals. The tuner in your TV works solely with Freeview signals. It can't handle FreeSat ones.
I'm also confused as to why you've subscribed to Sky if you only want a service similar to Freeview. FreeSat doesn't require a subscription. It simply requires a one-off payment of �150 if you need the dish and Sky box to be installed, or just �20 if you've already got them.
To get FreeSat through your new TV, you need a dual LNB, plus a second Sky box (under �20 on eBay) and a FreeSat card (�20 from Sky). You'll then get all of the channels listed here. (Use the scroll bar):
http://www.freesatfromsky.co.uk/?pID=3
The FreeSat line up includes both 'Free to Air' (unencrypted) channels and the 'Free to View' (encrypted) ones. Without a FreeSat card, you'll only get the channels marked 'FTA' here:
http://www.wickonline.com/fta.htm
Chris