Avast Pro AV 11.1.2245 - but, as I said, the problem has existed for many months, including a number of prior versions (meaning not 11.1.2245). And its not a problem with the router - I can get out over wifi from my smartphone when the PC is stalled. COuld be the router blocking for a while, but it doesn't seem likely to me.
And that question I mentioned doesn't happen now - I remember, vaguely, it happening once when I was installing some software - maybe AVast, maybe something else. So it's not some software asking what I want it to do with some new activity - it was something like "I can provide better security from now on if I block internet activity after a bootup, until I am ready to monitor everything - or you can allow internet activity for other programs if it happens before I am ready to enforce security." But I may be mis-remembering this whole thing completely - I am really asking if this question sounds familiar to anyone.
I am pretty sure I have checked what is running when this occurs - and it is all the normal startup programs. I'll check again, and I'll check the event log during and after this problem, the next time I boot.
Thanks
Dan