So, I'm getting the occasional CAPTCHA message, which is irritating but fine, but occasionally Google just blocks my network wholesale. I've submitted automated requests to unblock it, but I have no idea who I can email directly to clarify the issue.
I've run all manner of anti-virus, parsed my router's logs, combed through Fiddler to see if any errant packets were slipping by. Nothing. The only Google searches that happen are made by me through the web-browser.
Who or what do I have to do to get Google to stop falsely flagging my network as a spam-bot?
You may be behind a proxy provided by your ISP or government, which mixes in your requests with others in your local area, so that they can't easily be differentiated by IP address. Google should be smart enough to figure out this situation, but that doesn't always seem to be the case. Check to see if you're behind a proxy by using an online tool that shows your HTTP headers and attempts to detect the use of a proxy server (such as mine).
Have you considered the possibility that your computer is part of a botnet? They're designed so it would be hard for you to detect.
Use a different computer to download a bootable virus/malware scan disk and see what you find. Free of charge if you pick the right scanner.
using a vpn will cause this behavior as will tor. so it seems that if you like to protect yourself and your anonymity they make it a little arduous. i think they could determine the difference but they are in the business of data mining