I noticed in the TCPView log above that Port 135 was being listened to.
Well, after much research here and on the net, I found that an old concern on this forum & on the 'net in general, Windows DCOM Services (RPCss), runs whenever avast! is launched & might be the source of my problems.
After a little thought, I deleted this exe to see what would happen...
Sure enuf, my 'Ashwebsv Not Responding' issue went away.
I could shutdown normally, and, since I have Win98 where RPC is not mission-critical to the OS, everything was fine for the few days I ran like this.
The only problem was, as stated here many months ago, the avast! Virus Chest was rendered inoperative. Everything else worked perfectly..
Well, as much as I am impressed by avast!

, not having a Virus Chest is
NOT an option.
So I 'restored' RPCss back to the system folder and figured I'd live with the shutdown inconvenience.
Funny thing...that was 3 days ago, and I have not had the 'Not responding' problem since..!

Avast and Shutdown work perfectly....go figure.....