Hi and welcome to JustAnswer,Thank you for the question and your patience. Should you still need assistance for information purposes only...Initially, bear with us; re-confirm and post back with the complete model number of the laptop.
Additionally, will the laptop have sound if regular headphones are plugged into the green 3.5mm jack?
Is a cable with 3.5mm plug to 2 X RCA plugs attempted to be used between the 2?
Have you tried plugging in the 2 X RCA to the XV-DV303 rear's TV-AUDIO IN L & R jacks? If yes and when touching just only the tip of the cable's other end 3.5mm plug, is there a thump/humming sound from the connected S-DV303 speakers?
Please post back results / observations of the above once tried.