Okay, so I have an update. Despite my eagerness to avoid it, I did indeed nuke it. I backed everything up, did a complete format of the drive, and reinstalled the OS. I got the machine back to full working order, and had zero problems in the few hours I was working on it.
So I took the laptop back to its owner, waved goodbye, and was on my way. Sadly, that wasn't the end of it.
The owner called me 3-5 days later to tell me that he was having the same issues he was before (minus the ultimate lack of being able to log in, fortunately). I went over, looked at the computer, and it was that great diagnostic problem where everything worked fine for me, but sure enough a couple days later he's called again with slowness issues. He says that it will just slow to a crawl, where he's still able to do things, but it'll take much longer to do them, like 20 minutes to send an email. I'd installed a trial copy of NOD32, and it only found two minor virus files in the temporary internet files of his backup data, but otherwise it's clean.
Any ideas what might be happening? I did my best to find a polite way to ask if he'd done anything stupid after the reformatting that he might have also done previously, but he couldn't think of anything.
I'm a bit stumped...
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Matt