@mrsandiego you still did not tell us what '''model''' your TV is. Anyhow you are wanting to connect the S-video to the computer and the TV, so I assume that your TV at least has a S-video connection. Your HP Notebook seems to use a HDMI port as well as a VGA port. Check to see if your TV has that connector. If it does, get a VGA cable and simply connect it from your Notebook to your TV.
If your TV does not have a VGA port, you will need a HDMI-to-S-Video adapter. Of course, if your TV has RCA input you can simply purchase a HDMI-RCA video cable.