All you need is the 1/8"(3.5mm) male stereo to male stereo cable long enough to reach from computer>TV and the Y-splitter to allow you to keep the computer speakers plugged in. You will be plugging the splitter into the green port you were using for the speakers.
This type of cable. Whatever length you require.
You simply need to set the volume level on the computer to a level that sounds about the same as the other sources you are viewing on the TV, and the TV volume control will control the audio level coming out of it's own speakers as normal.
As I mentioned, to control anything on the computer itself while viewing from the TV, you will need something like a wireless mouse or computer remote control or wireless keyboard. Unless, of course, you are placing the computer near enough to the TV viewing area to reach with corded keyboard/mouse. Once you have the computer hooked up to the big screen, you may find that you'd like to use it that way for everything :).