I've got a Harman Kardon Soundsticks II sound system connected to my laptop since a while now. I was always happy with it, but lately I got some loose connection on the speakers. Nick Brook had similar issues, but his blog doesn't seem to be maintained anymore. I could find it on archive.org though.
I followed his recommendations and used a SCART to S-Video/RCA adaptor, removed the SCART connector and cracked open the box. I cut the connector from the Kardon and checked the connections with a multi-meter. They seemed to be correct. Inside the adaptor the connectors are solder on a pcb, so I just had to solder the wires to the correct pads.
On the cinch connector, the red wire is the inner one and the black wire the outer one.
Below is a schematic representation of the S-Video and the pads on the pcb: