Thanks for the thoughts. For what it's worth, having tried your initial suggestions I contacted Symantec. I had a web chat, followed by a phone call and then a referral to econd line support, who called me back. He then logged on to my computer and has, to date, spent a day and a half remotely attempting to figure out what's up and trying to fix it; I don't think he's succeeded yet (although the effort is clearly immense!) and I'm guessing he'll be back in touch later today.
So if there is a solution, ultimately, I suspect it'll be unique to my particular circumstances - shame, really, because I'd have liked to pass on to the community whatever I'd learned. If it does turn out there's something worth knowing I'll add it here - but I'm not holding my breath!