Are the computer and the speakers plugged into the same power strip? If they are not, and particularly if the power strip has a surge suppressor or rfi filtering built into it, the resulting isolation could conceivably be the cause.
The other thing that comes to mind, which once caused me to have a similar problem, is simply poor contact between the mini-plug and the mini-jack. With the volume control on the speaker set fairly low, try jiggling the plug and see if that affects the hum.
My feeling has been that 1/8 inch mini-connectors, and also 1/4 inch headphone jacks, are abominations. Unfortunately, they seem to be unavoidable these days.
Regards,
-- Al