Sounds more like a grounding problem than transformer noise. Could be that your speakers really are not made to handle your particular headphones. This could stem from an impedance mismatch: your speaker output probably cannot handle the high impedance (like resistance) of your headphones.
If you even think you want to use headphones, go here:
http://www.headphone.com
and get their entry-level headphone amplifier.
OR:
Just move your computer and plug the headphones directly into your sound card. That should easily bypass the problem.
OR:
Get better speakers. Seriously. Why spend $99 on a sound card, and under $10 on speakers, especially on a new rig? Don't do it!