To keep it simple, the hum comes from electronic interference in your computer (barring equipment failure). Yes you can probably solve the problem by getting a new sound card (X-fi series seems worth looking into) but it is by far better to separate the Analog conversion from your computer.
A reasonably priced external solution is a Zero DAC/AMP (simple terms - a external sound card with a small amplifier built in) off ebay (chinese, but very high quality) for about 140-200$. It is a solid state Headphone amp that can also function as a Stereo pre-amp and has a good DAC and opamps in it which can also be changed if you want to alter the sound or upgrade the DAC/opamp.
Since you don't seem to use a receiver you may also consider that instead, esp one with pre-outs if you want to continue using external amps. That won't run you much more than a Zero.
However if you just want to get rid of the hum the USB thing sholling recommends will probably work, I just can't attest to the quality of any DAC in them.
And as far as digital output from a computer, generally all sound is converted to 2 channel PCM (including games, mp3, etc.) if it isn't DTS or AC3 (which still has to be set to 'pass-through' in the program so it isn't down mixed to stereo). Again this depends on the sound driver used for your card/onboard sound. I'm sure there are some exceptions that don't default this though.