I fiddled around the zone where you thought the problem lay in.
I deleted two existing user accounts leaving my own admin one
I turned on the guest account
I made a new account under limited status
I made a new account giving it admin status
I logged onto all accounts then logged off one by one (except my admin). The new limited and admin accounts logged off okay but the guest account gave the same old grey window up (the Norton-associated: Ending programme "ccAPP..." entitled window) but logged of reasonably quickly..
I rebooted, logged into all then logged off one by one and this time they all logged off straightaway!
Test time. I logged into all - then switched to my original admin account and attempted to shut down from there. And it did - at a decent speed too.
Top marks for the pinpoint Al..asdair - even if I still can't figure out what the hell is going on.
iano