The problem was this: all attempts to connect through the LAN via Remote Desktop from Windows 7 were met with "This computer can't connect to the remote computer. Try connecting again...etc."
The Server 2012 Standard (not R2) computer is running the most simple Remote Desktop mode accessed through Computer/Remote Settings as shown below.
I went through rabbit trails with firewall settings, Remote Desktop Services (which I did not install) turning on and off the 'Allow connections only from computers running Remote Desktop with Network Level Authentication', using Select Users - none of them worked.
During extensive searching I ran across a some discussions of TLS and RDP on Windows 7. I found that we had RDP 7.1 on the Windows 7 sp1 computer and RDP 8.0 was an optional download through Windows update. RDP 8 apparently has support for later TLS versions beyond the disabled TLS 1.0. RDP 8 for Windows 7 is discussed here: https://support.microsoft.com/en-us/kb/2592687.
Solution: After installing the KB2592687 update (an optional update in Windows update), rebooting and installing even more updates triggered by that update, RDP 8.0 client was installed and connected normally to the Windows 2012 server.
There is also an RDP 8.1 client only update KB2830477 that I may install later but for now I can Remote Desktop in to the Server 2012 box from Windows 7 without any apparent problems.
More info on RDP 8.1 for Windows 7 including prerequisites: http://blogs.msdn.com/b/rds/archive/2013/11/12/remote-desktop-protocol-8-1-update-for-windows-7-sp1-released-to-web.aspx
