So I'm writing this up so if it happens again I won't have to spend another seven hours figuring it out all over again.
Problem: Windows 10 client machine could not see the server PC for file or printer sharing. net use \servername gave error 53 "Network path not found". The server PC could see the client PC fine. The client could PING or use NET USE with an IP address no problem. But I couldn't print or map drives using the machine's network name.
Clue: nslookup servername on the client PC returned an ip address for servername.netgear.com!
Solution: As it turns out, Windows by default appends the "domain name" it thinks it is on when you type nslookup computername where computername isn't a fully qualified domain name. In my case it was asking my DNS server for the IP of servername.netgear.com. That led me to learn that when a computer requests an IP address via DHCP, it also gets assigned a domain name. On my router, the configured default domain name for DHCP was netgear.com! This worked fine for all my other PC's whose names didn't happen to be a computer on netgear.com's network. I changed the DHCP domain on the router to my actual domain and problem solved. In theory, any domain that doesn't exist should work fine so that the DNS lookup fails and Windows falls back to WINS (which I determined was working fine by using nbtstat -a servername.)
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