Hi mskh4n and welcome.

Have you tried looking at the connection diagrams in your iManual here: -

http://pdf.crse.com/manuals/iManuals/eng/CX52x_o32/nt_wiredlan.html

Basically, I think you need to connect the TV to your router to access the internet features on your TV.  To do this you can either use the Sony WiFi dongle or, if your wireless connection is weak, you can connect by ethernet cable using a set of homeplugs like these: -

http://www.amazon.co.uk/TP-Link-TL-PA211KIT-200Mbps-Powerline-Ethernet/dp/B004INVKP4/ref=sr_1_1?ie=UTF8&qid=1342477169&sr=8-1

I use these even though my TV has wireless built in as it gives a far more stable connection.

Your TV's internet features then work without your Vaio by communicating direct with your router.  However, you can set up your Vaio as a media server to stream video, Photos and Music from the Vaio to the TV.

http://pdf.crse.com/manuals/iManuals/eng/CX52x_o32/nt_cnttohomenw.html

Have a look at Catmambo's excellent Smart TV FAQ sticky thread here: -

https://www.sony.co.uk/discussions/message/763566#763566