I faced this problem when I was trying to connect to SQL server 2005 from another machine.
The error message said, that SQL server does not exist or access denied.
- Start SQL Server Configuration Manager
- Expand SQL Server network configuration
- Select Protocols for MSSQLSERVER
- Double click TCP/IP in the right pane.
- Change enabled to true
- Click IP Addresses Tab and change the IP address to the IP address of the client.
Start SQL Server Area Configuration
Select Surface area configuration for services and connections.
Go to Database Engine -> Remote Connections and verify that remote connections are enabled. (The correct radio button is selected)