Problem with Logitech Z-340 speakers

I am guessing there is electrical interference, especially given the problem manifests with two different cards. It could be many things. Look for a radio (AM/FM), a lighting fixture (especially one with a transformer or dimmer, or fluorescent), a relatively strong electromagnet, or a power cord or supply that is too close in proximity to the speakers and/or their wiring. You might even move all other such things far away, see if the hum ceases, then add them back one at a time.