Lsdmeasap,
You were kinda right. In the end, I had no option but to merely experiment with the settings and found that changing "Shutdown Wake-on-LAN" from Enabled to Disabled did the trick. The requisite Ethernet channel indicator on my Netgear DG834 router now extinguishes (as indeed logically it ought to) when I turn off the PC (the router, of course, is always left powered up by me), and comes back on each time Windows reboots.
I've also changed "WOL and Shutdown Link Speed" from 100M bps to 10M bps, though frankly I've only a vague notion of what that does. Given that my ADSL line syncs at no more than 4M bps, I can't see much point in my having a 100M bps Ethernet connection, especially as it's a wired one and only about 1 metre in length. I've wondered for a long time whether this 100/10M bps setting has anything to do with my browser's (IE) apparent inability to sometimes not find a website from the address bar. When I try it a second time, it succeeds. Other than that, it's perhaps a minor bug in the router's firmware causing it.
I've also wondered about "Green Ethernet" in the Realtek LAN port's settings. Does that have a bearing on disabling the Ethernet channel when you turn off the PC? Without there being a set of plain-english definitions of these cryptic settings, there's no way of really knowing. I've searched the Web for this but found nothing. Realtek themselves don't seem to publish anything much about the settings.
Anyway, in case this proves useful to others in the future, these are the settings I'm now using:-
802.1Q/1p VLAN Tagging - Disabled
Auto Disable PCIe - Disabled
Auto Disable PHY - Disabled
Checksum offload - Rx and Tx Enabled
Flow control - Enabled
Green Ethernet - Enabled
Jumbo frame - Disabled
Large Send offload - Enabled
Network Address - Not Present
Shutdown Wake-on-LAN - Disabled
Speed and Duplex - Auto negotiation
Wake-on-LAN capabilities - Pattern Match and Magic Packet
WOL and Shutdown Link Speed - 10M bps first