Is there anything in the Windows event log? What you mention is indicative of (choose your pick):
- a soft-lock in the kernel/driver subsystem (or at least it would be if this occurred on Linux),
- a frankly terrible harddisk controller, that locks up so there's no functional harddisk I/O for a while (this is a known issue with first generation SSD's based on JMicron controllers for instance),
- a power/heat issue which temporarily knocks out a device.

Now if you think it is the sound subsystem that is to blame, a quick and dirty workaround would be to see if routing all audio through the chip on your graphics card (required for HDMI with sound, which ATI cards support IIRC) makes the problems go away.
The set up would work like this:
(a) Connect your display via a HDMI cable and if you use external speakers connect them to the audio-out of your display.
(b) Configure windows (using the control panel) to route sound through the chip on the graphics card (probably represented like S/PDIF interface, i.e.: a box, rather than a speaker icon). You may have 2 or more of similar interfaces if your Azalia audio chip also supports a S/PDIF output (I'm guessing it does).

Alternatively fiddling with drivers (updating/roll-back) might help, too.