Here are a few things I'd consider:
* Can you ping the target server from the computer the package is running on? If not, the server may be down or there may be routing or DNS issues
* Is SQL Server Browser running on the target computer, or did you supply the port number in the connection string?
* Can you get a telnet session to the server using the port number? If not, SQL Server may not be running
* Have you spelled the server and instance name correctly?
* Does the target server have TCP enabled in SQL Server Configuration Manager?
* Can you connect to the server from anywhere else?