The referenced component 'System' could not be found. (or any other component for that matter)

I had the same problem. It turns out that something was wrong with NuGet. I removed the following part of the *.csproj-File (opened in a text editor). This has solved the issue for me:

<Target Name="EnsureNuGetPackageBuildImports" BeforeTargets="PrepareForBuild">
    <PropertyGroup>
        <ErrorText>This project references NuGet package(s) that are missing on this computer. Enable NuGet Package Restore to download them.  For more information, see http://go.microsoft.com/fwlink/?LinkID=322105. The missing file is {0}.</ErrorText>
    </PropertyGroup>
    <Error Condition="!Exists('$(SolutionDir)\.nuget\NuGet.targets')" Text="$([System.String]::Format('$(ErrorText)', '$(SolutionDir)\.nuget\NuGet.targets'))" />
</Target>

In my case, the solution was completely different. It looked like it was an issue with NuGet paths (caused by my moving the project to a different solution and then back again.

I edited the .csproj and removed all references to NuGet and associated packages. I also removed the packages folder from the solution folder.

The system components then magically reappeared.

Suggested next debug step: review Project Designer: References -> Reference Paths to verify that the paths to your system and third-party components appear correctly. (Watch out for things that can slip past the old Mark I Eyeball like drive letters.)