Jay,
I have not heard of this problem and I don't know. It sounds like a chipset hardware issue when under load. I had a look at some of the related Intel specification updates, e.g.
http://www.intel.com/Assets/PDF/specupdate/316274.pdf, and note that there are some issues related to DMA Transfer completion for DMA sensitive devices in some scenarios. Depending on your setup, maybe it is related to this.
Also,
http://www.intel.com/Assets/PDF/specupdate/313057.pdf, refers to
"Intel ICH8 Integrated LAN DMA Error" and "ICH8 GbE Packet Buffer Writing Error". Less likely I suspect.
I would look at updating your motherboard BIOS.
I would test XP on the same system. The specification updates do refer to specific Vista (and hence probably Win7) issues, but none seemed related.
It would be interesting to remove some load and only run the Network and audio tests to see if the problem still occurs. Also I don't know if both of your NICs are on the motherboard and you get errors on both NICs.
Regards,
Ian