Windows 7 PC can't see anything on the network

If you have this problem and go searching on the web you'll find a huge number of posts: it's terribly common.  So common that you'd have thought that Microsoft would have fixed it, but there we are.

Here's my experience today, which isn't as far as I can see the same as any of the twenty or so hits (none of them saying anything definitive) which I looked at this morning.

Symptoms

• Clicking on "network" showed only the local machine, the defined network printers, and an icon representing the NAS to which I was trying to get access.  Not the sort of icon that allows you to get at the files, though.
• Opening a command window and pinging the device by name (I haven't bothered creating a hosts file) worked fine, so the TCP/IP parts were working.

The cure

I can't call this a "fix" since it makes no sense.  In order to check whether some firewall rule was dropping the relevant traffic I turned the firewall off.  Bingo!  The network appeared.  "Ah, a firewall problem," I said to myself.  "Now what on earth is causing that?"

I turned the firewall back on again, and the network was still visible.  Job done ... but why?  Oh well, Windows is like that.