To solve this you must ensure the following is true on the machine hosting SQL Server...
Ensure Server Browser service is running
Ensure TCP/IP communication is enabled for each instance you wish to communicate with over the network.
If running multiple instances, ensure each instance is using a different port, and that the port is not in use. e.g for two instance 1433 (default port for the default instance, 1435 for a named instance.
Ensure the firewall has an entry to allow communication with SQL Server browser on port 1434 over the UDP protocol.
Ensure the firewall has an entry to allow communication with SQL Server instances on the ports assigned to them in step 3 over the TCP protocol