Thanks for taking an interest.
I can't quite remember the last Avast screen - it was yesterday, I was rushing. I think it offered registry clean up - I looked for options, but there weren't any. I trusted it, so went ahead, then ran out the door to work.
Meanwhile, I've just had a pop-up from Windows saying 'thanks for updating to Windows 10' which is odd, because I installed W10 a couple of months ago. Do you think these symptoms could be from a new (unasked for) install of W10? It seems odd that it would happen in the same restart period as Avast, and that Avast browser would appear and everything else disappear at the same time. However, the second evaporation of Dropbox in the last couple of hours suggests it might be an OS problem (I don't think Avast gets off without blame thougt)