The headphone thing could be your problem.
After you fix the headphone problem, start at the furthest point from the computer (whatever is plugged into your mixer), and unplug one thing at a time (I mean audio cables). When the hum disappears, you've found your problem. From there, you can try changing the last patch cord you unplugged. If that doesnt help, and the unit's power cord has a 3 prong (grounded) plug get a 2 to 3 prong adapter (everybody has at least one of these floating around the house) and plug the unit in using that.
Wire routing is another issue. Most people like to organize their wires in nice neat little bundles. Looks real nice. Horrible for audio. Keep your audio cables and power cables seperate. If they need to cross paths, do it at 90 degrees. Don't run them along side each other.
Computer monitors are also known to induce noise in the audio chain. If your mixer, effects, guitars, mic, etc.. are close to your computer and/or monitor, try simply moving them further away. Also bear in mind that you will almost never get rid of hum or buzz generated from single coil guitar pickups.
Before every connect/disconnect/move, make sure you turn off any amplifiers or preamps. You don't want to get any loud pops as you're plugging and unplugging.
If you find a particular peice of gear is creating noise and none of the above works to get rid of it, there are a few more options, though they get a bit more involved. Try these first and see what happens.
