I moved from a work laptop on Windows 7 to a work laptop on Windows 10. I had been successfully using SSMS2016 on Windows 7.
The same issue applied using SSMS2012 or SSMS2016. My access to the 10 sql servers using windows authentication was still the same. I could test this from another server. However, 2 of the 10 servers would not connect from my laptop. Both were ms sql server 9 but I could connect to other sql server 9 databases.
The solution was to add a firewall rule (using Windows Firewall with Advanced Security).
Create an Incoming rule for each SSMS eg C:\Program Files (x86)\Microsoft SQL Server\130\Tools\Binn\ManagementStudio\Ssms.exe
I'm not a network expert so I've not included the details but hopefully it will point you in the right direction.
Error msg (pre firewall rule) "A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: SQL Network Interfaces, error: 26 - Error Locating Server/Instance Specified) (.Net SqlClient Data Provider)"