The "deploymentfiles" downloads are pre-compiled and meant for production deployment to IIS Web Server, not really intended for use in Visual Studio, though it can work in Visual Studio 2010 (opened as a web site not in a project), it has no C# source code, it is all pre-compiled. I've never tried using those files in VS 2008 but it should not be using a project file since there is no source code it must be opened as a web site.
Visual Studio won't see the connection string because we don't use the <ConnectionStrings section but use <appSettings for our connection string.
For those who want to work with Visual Studio, I recommend use the source code not deployment packages and it requires Visual Studio 2010 or the free Visual Web Developer Express 2010
How can I possibly know if your connection string is correct?
I will say that I always use a sql user and password not a trusted connection myself because this is what is needed for most hosting situations, so the format of your connection string is not what I use. Also parenthesis around the server name seems questionable.
Hope it helps,