Open Visual Studio 2008 Solution in Visual Studio

In short: I need to open an application originally built in Visual Studio 2008 (version 9) in Visual Studio 2013 without upgrading the project since the overall project architecture must remain the same for when I check it back into source control.

Details: I need to open a Visual Studio solution (.sln) inside Visual Studio 2013. The solution in question was originally developed in Visual Studio 2008, so when I try to open said solution in Visual Studio 2013, I am shown a prompt with the projects within the solution checkmarked, with the message:

These projects are either or supported or need project behavior impacting modifications to open in this version of Visual Studio. Projects no displayed either require no changes or will automatically be modified such that behavior is not impacted. Visual Studio will automatically make functional changes to the following projects in order to open them. You will not be able to open these projects in the version of Visual Studio in which they were originally created.*

My attempt at a fix was to just upgrade the solution and hope for the best. This is successful, but after building and attempting to run the main project, I see the following build error:

The type 'Microsoft.Web.Services3.WebServicesClientProtocol' is defined in an assembly that is not referenced. You must add a reference to assembly 'Microsoft.Web.Services3, Version=3.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35'. *

I then tried both commenting out the references to this assembly and adding in the missing reference. Okay, so then I rebuilt the solution and attempted to run. Same error, but for a different assembly. Repeat fix, same error for different assembly. This pattern continues and continues, and at this point I realize this is unacceptable anyway, because when I make a change to this solution, I need to check it back into source control. When others open it, they may be opening it in VS2008, and therefore this “upgraded” version is inconsistent with the version the business uses. I need to open the solution originally build in VS2008 in VS 2013 (can't work around this, needs to be VS2013). If it helps, I'm using 64 bit Visual Studio 2013 Ultimate.

Any help or guidance will be greatly appreciated!

As several of the commenters have already helpfully pointed out, this is not possible. Round-tripping (i.e., opening and manipulating project files created by an older version of Visual Studio in a newer version of Visual Studio) was not supported until Visual Studio 11. The only way to open a Visual Studio 2008 project/solution in a later version of Visual Studio will be to convert it.

As far as interoperability with previous versions is concerned, you have two options:

Update the project locally (using the migration wizard provided), make any changes to the project file necessary to get it to build, and then edit the code files. Once you're satisfied with your edits, commit only the modified source files, not the project infrastructure files. Your fellow developers, stuck on VS 2008, won't notice any difference.
Update the project locally (using the migration wizard provided), make any changes to the project file necessary to get it to build, and then rename the project file (e.g., by appending a -vs2013 suffix to it). Commit this to your code repository. You will now have two project files in your root directory, one for each version of Visual Studio that your team works with. From here on, you just open the project file corresponding to the version of VS that you have installed.

I used approach #1 for a good part of last year, where I spent most of my time developing a C++ application in VS 2010 on a desktop machine, but also wanted to work on it on my notebook running VS 2013. Of course, in my case, it took a trivial amount of time for the automatic conversion to upgrade my project file after pulling from source control. I didn't have to do any tweaking thereafter to get the project to build. It sounds like your case is different, so option #2 might be a better choice.