If you are experiencing a problem connecting to your SQL Server 2008 R2 DB server from any remote machine in your network, Please make sure of the following:
1) You are able to ping the machine from the remote server.
2) Try to connect make sure that the SQL Server Engine service is up and running, You can open "SQL Server Configuration Manager" and make sure that the service is up and running.
3) Make sure that you have at least one protocol TCP/IP,Named Piper or Shared Memory is allowed on both your client and your DB Server and this you can check it from SQL Configuration Manager.
4) THIS FIXED MY PROBLEM: Disable the Domain firewall in the DB machine that blocks all inbound connections to your DB Server. To do this:
a) From Server Manager.
b) Under Configuration - > Select Windows Firewall.
c) Click on Windows Firewall Properties and disable your domain profile firewall.
Try to refresh your page and you will be able to connect to your DB.
Hope this helps.