I did a test with my machine disconnected from my network. I loaded a solution file that contains a
VB.NET web application and a C# web application. I did get a couple errors because all my projects are under source control and it tried to update the status of the files. Apart from that, they loaded fine.
Are your projects under source control? The only other thing I can think of Brian already mentioned. You shouldn't need to work "disconnected". Is it possible there is some security issue and your machine is trying to authenticate you against a domain?