Validating with login server
To confirm that firewall is blocking the connectivity, use Port Qry from
Family ID=8355e537-1ea6-4569-aabb-f248f4bd91d0&displaylang=en Here is a sample output when I connect to a server name SQLMOSS (This should be a node name if it is a standalone instance and virtual server name if it is clustered instance) If you don't get any instance names returned in the result set, it should be firewall blocking the traffic.
You can change this to make SQL Server to allow Mixed Mode Authentication (Both SQL logins and Windows logins) from SSMS - Server Authentication.
So by now, hope you have the complete flow of how connectivity happens from a client to SQL Server. To make sure SQL Server Browser is able to start (Port 1434 is available for SQL Server Browser to grab), you can try start SQL Server Browser from command line : C:\Program Files\Microsoft SQL Server\Shared This step will ensure that SQL Browser works fine.
If you are able to start SQL Server Browser from command line and not as a service, check the service account configured for SQL Server Browser.
So SQL Server Browser knows the TCP port is say 1488, it will return this information back to the requested client that SQLMOSS instance is listening on port 1488.
Now the client will reconnect to SQLMOSS instance using the TCP port 1488 and provided there is not firewall blocking, this connection will succeed.