For the speakers, you need only connect to the GREEN jack at the back of your computer. It's OK to leave the others blank.
Your two HK speakers will, with one wire, connect to each other and, w/ another wire (usually having a GREEN connector on the end), connect to the computer.
I'm not sure what the 3rd wire is unless it's (1) the power connector or (2) for connecting to a sub-woofer.
Does the speaker set include a sub-woofer? Or does it include a "surround sound" or 3rd speaker?
You can find pics & symbols (the symbols are helpful if your sound card jacks are not color-coded) for (3) of the most common audio connections HERE
Usually the color of the connector on the wire is matched to the sound card jack w/ the same color. (green to green; pink to pink; blue to blue).
green = speakers
pink = mic
blue = line in
Make sure you are connecting to the active sound connectors - the ones you used b4 the HK speakers.
If you have "integrated audio" (audio that is built into the motherboard) and you have an audio expansion card installed on the computer as well, one may be disabled or not selected in your computer's audio configuration.
If that's the case (that you have two sets of audio jacks to choose from), try connecting the speaker wire from the HK speakers 1st to the green jack (or the jack marked w/ the symbol of a speaker) at the bottom of your computer. (There'll only audio jacks here if there is an audio expansion card installed on your computer.)
If that is the case, there'll be other (usually) colored jacks running horizontally next to the speakers jack.
If you still have no sound, connect the speaker wire to the GREEN jack that is (usually on Dells) up by your PS2 (round - one purple and one green) keyboard and mouse connectors (also at the back of your computer). The other jacks in that set (of audio jacks) will be situated vertical to one another and on the left-most side at the back of your computer.
Please, let us know if this response was helpful for you or, of course, if you have any further questions.