You will need a way to physically connect the PS3 to the computer.
The PS3 has connections for HDMI, and RCA. I believe you can buy a separate adapter for S-Video. Then you need to connect this to your computer, that has input for one of those plugs. This is where the TV-Tuner, video editing card on your computer comes in.
Otherwise, you would need a DVD recorder box or similar, to capture images on your TV set.
You don't have either, and the PS3 does not yet have the capability to record your games in this manner (although Sony promises to add this feature I believe). So my guess is you are out of luck, unless you have a camcorder, or digital camera that can record video. That would be crappy quality though.