Thanks for those links. I've bookmarked them and will check them against my settings. In the meantime though, as Sinatra once sang, "I did it my way". First, a spyware check with Spybot and AdAware, and then a complete deep virus scan. All negative. Then using GoBack, which has saved my *&^%! about a hundred times, I reverted to the start of the day. Everything worked fine with the proxy connection enabled. Finally, just to satisfy my curiosity, I downloaded the latest virus definition (which GoBack had removed), and again no problems whatsoever with Moz or IE, at least so far.
So the process was a little short on detective work, but I think things are fixed now. Thanks for your timely response, and if this story isn't over I'll certainly post back.