ok im almost sure that is powered, you need to see if you can connect the phono left and right output into a channel on the mixer, then raise the volume level and then the preamp level entil you get a loud enough signal of music from the turntable...
then depending on the input on your soundcard, you may have to go back to radioshack ;) and get the infamous "Y" cable with left and righ phono on one end(out of the mixer) and a 1/8 inch jack on the other(which goes into most soundcards on computers)
once again it depends on that kind of inputs and outputs the mixer has (1/4 inch, XLR, phono)
i cannot find any info on the Radio Shack DSM-8040