[Skip to end if you just want the solution that worked for me.]
Next suspicion was that my network interface card in my Dell computer had died. It is a “Intel 82567LF-2 Gigabit Network Connection”. However, the signs wasn’t there that it might have died. Nothing wrong with it in Device Manager (Right click “Computer” and choose “Manage”).
Windows did recognize the difference between disconnected cable (red cross for network icon in task bar notification area) and my currently unsolved problem (yellow exclamation point) and “Unidentified network”. Also, the network cable lights at the connector seemed to work fine (at least they was lit). Still no network and no pings working. Trying to ping the router or another computer in my network timed out or gave “Destination host unreachable” from the local network driver.
The network had died just when I started Spotify, so I was now starting to suspect that it was something wrong in Windows. I have Windows 7, 64-bit. Some sort of configuration that had gotten the hiccups? I found some commands (“netsh”) that can reset the Windows tcp/ip info, but it did not help (after reboot). I removed the network interface card drivers in Driver Manager and restarted, at which point the drivers were reinstalled automatically, but the problem remained.
I also read that something similar had happed to someone and that he had reinstalled all of Windows and thereby gotten it to work again. Not something you really would want to do.
As a side note, my HTC Hero proved useful since I managed to copy the Android Phone drivers from my laptop to the desktop computer and thereby I could get online using my shared connection facility of HTC Hero and its usb cable. Nice!
Anyway, it struck me that network interface cards actually flash their lights when the power of the computer is off. So maybe it is the firmware in the Intel card that had gotten the hiccups?
So I shut down my computer and removed the power cable for a few minutes. Then I started it again, and what do you know:
It worked again!
Update: I finally got this error a handful of times and have now installed the following from Intel (not from Dell, since that download said that I already had the latest drivers). We’ll see if problem goes away completely or not. After this install, the driver version went from 10.0.0.2 to 10.1.6.0.