I had similar issue after copying solution to another machine (we have different networks at work). Referencies were broken even though I could start the project in debug mode.

I opened some of that projects, specifically the ones I'm working with, in Solution Explorer I opened the Dependecies of the project -> then Project Referencies -> right click and chose Add project reference.

In that window I just added reference to any other project, clicked Ok. Then I opened Project Referencies again and removed that reference. All other referencies fixed automatically.

I began doing it for couple other projects, one of them I also rebuilt. And suddenly Visual Studio started restoring all the projects in solution magically, and all the references automatically got fixed.