"A project with an Output type of Class Library cannot be started directly"

I think it might have something to do if there are multiple projects in the solution. I was getting the same problem when I had a MVC project and the testing project in the same solution. What fixed it for me was setting the MVC project as the StartUp project. This is done by right clicking on the MVC project and selecting "Set as StartUp Project".

This works for VS2013 Professional

I had the same issue and corrected by altering the projecttype guid. Here is an example:

<ProjectTypeGuids>{349c5851-65df-11da-9384-00065b846f21};{fae04ec0-301f-11d3-bf4b-00c04f79efbc}</ProjectTypeGuids>