I apologize for taking so long to get back to this. A year ago I thought that being retired meant I would have more free time than I knew what to do with. How's that for being naive?
Can you plug the netbook directly into the router with an Ethernet cable?
Yes, I can. I unplugged the Ethernet cable from my printer (which works with no problems) and plugged it into the netbook.
If yes, turn off (disable) the netbook wireless, and test with a wired connection.
I don't know how to disable the wireless...

Oh, wait -- Uncle Google to the rescue (Fn+F9), wireless is now disabled, but still no internet connection wired directly to the router.
Edit: My network connections dialog box says the wired connection is connected at 100 Mbps.
Edit: One thing I should have said in the original post is that the last time the netbook would connect to the internet was when SWMBO was using it in Turkey.
tanstaafl.