http://www.docs.sony.com/reflib/doc..._id=1®ion_id=1&DL=',600,560,10,10,'Manuals'
That's the user manual for your TV. It appears you don't have any VGA inputs, but do have an HDMI in that has a set of stereo RCA jacks associated with it for a non-HDMI audio feed. Page 12 has this image.
You with that, you have a few choices:
1) MiniDisplayPort-->DVI dongle, and then a DVI-->HDMI cable for video. For audio you'd need a 3.5mm mini-jack to RCA cable (easy and cheap to find) for audio.
2) MiniDisplayPort-->HDMI dongle (From monoprice) and an HDMI cable for video, with the aforementioned audio solution.
3) Monoprice sells an active adapter that takes your MiniDisplayport and USB audio and outputs a single HDMI feed (
http://www.monoprice.com/products/p...=10428&cs_id=1042802&p_id=5969&seq=1&format=2) For this, you'd buy the listed adapter and then an HDMI cable of the appropriate length.
Some people have mentioned issues with the solution I listed in #2 for the video feed, I think it's TV dependent. I have solution #1 in use at my apartment to connect my computer to my Samsung LCD TV and it works wonderfully, never had an issue.
Hope this will help!!
Here's a thread dedicated to solving issues just like yours, it contains multiple product links and whatnot:
https://forums.macrumors.com/showthread.php?p=8536817 What I've said above sums up all the details of the linked thread, but yeah...more info for you!