Good job on the troubleshooting. Unfortunately, since you've already ruled out the palatable (BIOS and driver
problems), only the unpalatable now remains.
I'd suggest a completely "vanilla" reinstall of the OS (no antivirus, no OS updates, no apps... nothing at all that's not on the Windows disc). If the same thing happens, try updating the NIC driver to the latest version provided by the manufacturer. If it's still the same - get yourself a different brand/model of NIC.
Torrenting is just about the heaviest networking activity that most hardware will ever see. Altough that doesn't cause any issues for healthy hardware, it's logical to expect that the heavy workload will potentially expose defects in not-so-healthy NICs.
If you can borrow a NIC from somewhere to test before spending money - so much the better.