Based on the connection string my first guess would be that your workstation is blocking the communication with the SQL Server. If this is for example SQL 2005, use the Surface Area COnfiguration to enable TCP/IP communication from outside your PC. Also check that the firewall in Windows doesn't block the communication
One good checklist to go through: How to configure SQL Server 2005 to allow remote connections
Also check that your ASP.NET service is run under an account that has an access to the SQL Server.