HEre what I did:
Use the RCA cables that you have and go to radio shack and buy an RCA to 1/8 inch stereo miniplug converter. THen you can hook up your mixer to the "line in" port of your sound card. Now you should be able to hear your mixing on your comp speakers provided everything is set up and configured right.

This will on work for front left and right speakers though so you will not be getting sound of the rears unless you find a different way to hook em up or tweak your soundcard settings to split the signal for you

you might be able to get the following adapters to go from mixer to speakers like you want (w/o computer in between)

- RCA --> 1/8" female stereo
- 1/8" male --> (2) 1/8" female stereo (make sure this one splits it off into stereo and not mono

now plug both your your speakers in there, 1 set to each jack. this should split the channel off into 2 rights and 2 lefts.

this seems like a lot more trouble than it is worth.