Windows 7: BSOD STOP: 0x0000001e

Security Software: ??? I see Sophos installed, but I do not see it running. Is it running, or is it even actually installed?

Make sure to install security software. I recommend either of these:

• Microsoft Security Essentials - Free Antivirus for Windows coupled with Malwarebytes. Do not start the free trial of Malwarebytes. Just use the standalone version, update it, and scan your computer once a week with Malwarebytes and with Microsoft Security Essentials.
  
  
• Good and Free system security combination.

After installing your security software, update it, and then run full scans today with each program. Report back the results of the scans.

Crashes point to your wireless network adapter. Yours appears to be a USB device with Atheros drivers (you may have a different manufacturer). I would advice replacing the USB wireless network adapter with a Windows 7 compatible PCI wireless adapter. If you cannot replace the USB device with a PCI device, at least get a USB device that is Windows 7 compatible; yours is from 2008 and is pre-Windows 7.

Keep in mind that if you do stay with USB wireless network adapters instead of PCI, they are inherrently unstable. USB ports do not supply adequate power for those devices to work reliably. You are much better off with a PCI device if you can find one that meets your needs and fits your system's hardware configuration.