Hi dpopiz,
I have the 621s too and I am learning to live with the constant hiss you're hearing. I personally find this unbearable when working in a silent environment and I wonder how "audiophiles" and audio review sites don't mention that.
It seems though that about every set of speakers on the market suffers from this (maybe except digital ones).
I had first bought the Altec Lansing 2100. Tired of the constant hissing (even unplugged from the PC), I thought they were defective and I tried exchanging them for another set. Same thing. I switched to the 621s, and although they sound much better, the hissing is actually a little worse. I tried them on other PCs and at friends' houses (to rule out radio interference), it's the exact same thing.
I guess the solution would be to put the speakers as far away from you as possible.
Tell me how it turns out, and good luck!