If you hear variable pitch noise that changes based on PC activity it is unlikely that you have a grounding problem. Ground loops typically manifest as a 60Hz hum that may vary in volume but never in pitch. You likely have an electrical isolation problem (EMI being transmitted where it shouldn't), which is not the same as grounding and can't be addressed the same way. I previously experienced the exact same problem that you're experiencing with a few different soundcards and the issue in my case had nothing to do with grounding, the PC noise was being transmitted directly through my soundcard to the amplifier.
The issue in my case resulted from a poorly electrically isolated DAC (soundcards inside my PC) hooked up to a high gain amplifier. What you are hearing is very likely the noise being transmitted to your soundcard through the PCI bus being transmitted to the amp and then amplified 20 to 30 dB. There are only three solutions to that kind of problem:
1) A better isolated DAC/soundcard: you can invest in an external DAC, an internal DAC with an alternative power source, or you can investigate some kind of PCI power filter. I would advise looking into external DACs as I have tried a half dozen internal cards including several with separate molex power draws, some of which were quite expensive and had (allegedly) spectacular noise performance. None were adequately isolated enough to hook up to a high gain power amp with very sensitive speakers. For example, I have an Asus Essence ST (which is a close cousin to your Claro), which has a separate molex power draw, and allegedly has a -124dBFS noise floor. In practice it picked up significant PC noise that I could hear through my speakers from across the room. The noise was exactly like yours (varied in tone and pitch based on CPU activity, and I could hear drives spinning up, etc.). I had the same experience with several other internal cards (I tested six in all).
Internal cards with analog outputs, even very high end ones, just aren't great at noise isolation in my experience, which is exacerbated when hooked directly to a 20dB or 30dB gain amplifier. Put another way, even a sound card with a respectable -100dBFS noisefloor only has a -70dBFS noisefloor once fed through a high gain amp, and if a -20dBFS audio signal is plenty loud on your setup, a changing pitch noisefloor at -70dBFS will be quite audible. And that's assuming that the specifications provided are "honest" (i.e. actually taken in a normal PC environment instead of a lab). External DACs/soundcards are, as a group, better in my experience even with equivalent published distortion specs, for that exact reason. if you can get an external DAC with balanced outputs, even better. As an object example, my current external DAC has a rated dynamic range of 117dB, which means based on specs it should be 7dB noisier than my Asus ST and about as noisy as my Asus DX. I can tell you from actual measurement that it's actually 10 to 20 dB lower noise than either of those two cards in any PC I've tested.
2) A passive in-line attenuator. This will push the noise floor of your sound card farther down (prior to the amp) so there will be less noise to amplify. This will lower your theoretical maximum output volume as well, but will result in significantly less noise coming out of your speakers at idle. They're available in different attenuation values, and you want to use as little attenuation as you can stand. Here's an example of the type of device:
http://www.amazon.com/Harrison-Labs-Line-Level-Attenuator/dp/B0006N41B0. Other than limiting headroom they should contribute no noise or distortion to the setup (other than some resistive heat noise way down at -140dBFS).
3) You built your amps (I built my own too!): if you can adjust the fixed voltage gain of your amplifier modules, try turning down the gain. Note that depending on where you placed your volume switch in your design you may be able to adjust the effective gain by adjusting the volume, but that may not be the case (it depends on whether your volume control attenuates at the input or the output). it may not be that easy depending on your design. In my case I had to pull a resistor.
I have a pair of 113dB sensitivity horns and I had to do all three steps to effectively remove all audible PC noise, no joke. I now use an external DAC with balanced outputs, 10dB in-line attenuators,
and I lowered the gain on my home-made amps. All three were necessary to get to "black silence." Two out of the three got me close, but I could still faintly hear noise when nothing was playing (a soft hiss).
113dB sensitivity is an extreme case though, with a speaker with a normal sensitivity you might only need to do one or two of the options. The in-line attenuators are by far the cheapest solution if you can spare the headroom, unless you can easily adjust your amp gain.