You have to connect the PS2 leads to the line in on your soundcard too, if you can. Or there may be a line out socket on the Dazzle to connect to your line in on your soundcard.
I've got the yellow video phono socket connected to my graphics card, and the red and white sound sockets connected to the line in on the soundcard.
EDIT: I think I've mis-read your question. I see you have sound on playback. There may be an option in the recording software that you are using to mute while its recording.