I have just downloaded the projects from the article you mention (Customizable MonthCalendar Type Control: Part 1
]) and they work fine.
Note that I am using VS2013 so I had to create a new solution. First I loaded the project MPK_Calendar. Visual Studio did an automatic one-way converstion for me. I then built the project to check everything was Ok (it was).
Then I added MPK_Calendar_demo to my solution - again this was converted by VS.
I had to manually add a Solution reference to MPK_Calendar in the Reference section of that project. I was then able to successfully build the entire solution.
Making sure that I set Calendar_Test as the Startup project I was then able to run the demo. Selecting the button "Selected Day Color" changed the backcolor of whichever date I then clicked.
I suggest you attempt the same steps as me (in the same order). By all means come back if you still can't get that code to work.