Regarding my set up, I do have USB 3.0 and a hub but still get the BSOD whether they are in use or not.. As jw300 mentioned above I also get the BSOD with just the QBox II, mouse and keyboard connected directly to the motherboard through USB 2.0. ports (not 3.0 ports).
However, although I still have problems I do appear to have found half a solution....
On one attempt to get to the bottom of the problem I installed all the dvblink software and tbsviewer provided with the QBox II and although I'm not using either application (I'm using WMC7) the computer has bluescreened only a couple of times over the two months. It does still give a power transition error just prior to sleeping, and also now wakes up for no apparent reason (the log mentions waking due to an unknown device). It now also fails to idle to sleep predictably (generally takes several hours dispite being set to sleep after half an hour).
The key thing - a few days after uninstalling the dvblink and tbsviewer applications the computer started to crash again. Reinstalling them prevented this.
In case it's useful, one thing I noticed that's different with dvblink/tbsviewer installed, compared to when it's crashing, is a satellite channel without a signal produces a black screen in windows media center (as if the QBox is providing a 'black screen' rather than no signal at all). With dvblink/tbsviewer installed a channel with no signal shows a WMC7 text warning of there being no signal.
Hopefully this information is helpful, if you have any queries let me know, I'd love to solve this once and for all.