Fixed! (I think) by Yoshinkeru at 9:59 AM EST on February 23, 2013
Good news, gang: I think I've licked it.
Nothing here worked, though: That AVG CD didn't find a thing other than a few things in Java it thought were "viruses". (I went ahead and tried to clean them anyway; from the directory, it looked like an old version)
It's starting to boot more stable now, and it seems Microsoft Security Essentials is more consistent with its warning: Turns out, I had a Trojan rootkit called Alureon. Still couldn't get the offline Defender to work, though, so I did some research, and a recommended program was TDSS Killer (which seemed to be on here already? Can't remember when or why I got it...) Ran it, and it came up with something (though it called it something else), attempted a "clean", rebooted, and lo and behold, the connection seems just as fast as before!
Weird thing, though, is that right after starting up again, Windows installed a SCSI driver of some sort (referencing a drive TDSS Killer mentioned the rootkit was in); maybe that's where it screwed up? And it does remain to be seen whether this crops up again if I restart this thing again...