It sounds like it may be related either to your ISP or Wifi AP / router settings, for instance NAT or proxy settings. I'd start with a simple test: can you actually resolve the DB server ('nslookup'), and if so, can you reach its IP address ('ping', 'traceroute', 'nmap' or such), and if so can you reach the listening port (default for the MSSQL DB engine is TCP port 1433)?
Here's a cool post on how to test TCP connectivity (either using telnet or PowerShell):

How to check Port 1433 is working for Sql Server or not?

I hope this helps.