I know that SQL Server is running, why can't I connect to it remotely?

There could be several reasons for this.
First of all, the
default SQL Server port of 1433 is blocked at our border routers for
security purposes. Therefore, the port that SQL Server runs on will
need to be changed.

1. You can do this by opening the Server Network Utility. (Start -> Programs -> Microsoft SQL Server -> Server Network Utility)

2. On the General tab, make sure TCP/IP is highlighted, and click Properties.

3. Change the port to 1434.

4. Restart the SQL Server service.

Also, on your PC youâ€™ll need to make sure youâ€™re connecting with TCP/IP on the correct port.

1. Open the Client Network Utility (Start -> Programs -> Microsoft SQL Server -> Server Network Utility)

2. Make sure TCP/IP is the only protocol enabled. If Named Pipes is listed, remove it.

3. Go to Properties for TCP/IP and change the port to 1434.