I'm a little confused by your question (see my comment), but if you are wondering the best way to use SVN to manage the development of your ASP.NET website, I don't see why you can't include the solution file directly in the SVN repository. When your developers want to work on SVN, they sync with the repository and bring down the entire solution (including source, SLN file, properties, etc). Then, they can work locally on their machine developing the website.
Again, your question is a bit confusing, so I am not sure how else to answer.
Update
Thank you for clarifying your question. If the laptops do not have access to a local server you can do one of two things.
If you want to use Subversion, you can setup a server that is internet-facing - AKA, it's accessible from the net. However, this does require a little bit more work as you will need to have an address for them to point to, etc. But, in essence, this is no different than accessing on a local network, it's just a different address.
Another possibility is to use a different type of source control. Git or Mercurial comes to mind. Both of these products are distributed version control systems. Basically, if you aren't connected to a network, you still "submit" your product to the control system and, then, when you can connect back to the network, you merge your changes in with the main system on the network. It works very well (though is a bit more complicated to understand than Subversion).
Hopefully that helps you. (And, if it does, you can accept this as an answer to your question, which I would appreciate.)