Relative ConnectionString for SQL Server 2005 Express

I am creating a application in Visual C++ 2005 that has database connections in it. I have gone through the process of setting up the data source and it will work great on my computer. However, the second I move either the project or the created executable to another computer the application keeps crashing. I know that it is crashing due to the database connection string. The string is setup to work only on my computer, I am wondering how do I make, or edit, the string to work on any computer? Thanks for the help.
Have you gone into SQL Server Surface Area Configuration to enable remote connections to the database?