Do these speakers have a power switch on them? If they do, then they're active speakers, and should work plugged directly into the soundcard.
If they have no switch on them, and just have the cable from the soundcard plugged into them (ie, no power cable to speakers) then they are passive. The signal produced by any sound card is nowhere near loud enough to drive passive speakers directly.
If you can hear the buzz from tapping the mini-jack from the speakers on your palm (while switched on, if they have a power switch), then they're active, and the problem is one with your soundcard/drivers. Plug the speakers into an ipod or similar to check they're working.
To check the sound card is working, plug a set of headphones directly into the same lineout port you've been using on the soundcard - they'll be deafening, so don't wear them at the time (be certain you're not plugging into a line-in, or mic-in or something, obviously you won't hear anything if you are).
Then use your skills of deduction.