Update: I've tried the only fix I can find anywhere online, which involves downloading a Windows update. The reason I long ago disabled automatic Windows updates is because they invariably cause more problems than they fix. I downloaded the update and found that alt + tab no longer worked, and neither did the Windows icon in the bottom left-hand corner of the taskbar. Okay, I thought, I'll finish sorting the e-mail problem and then fix the other stuff. Unfortunately, following the rest of the instructions to fix the e-mail problem didn't work in any case, and I found myself having to do a system restore to undo the damage the Windows update had done.
Anything that will fix the problem without creating worse in it's wake would be gratefully received. I can't be the only one who's come across this.