Okay, I just realized I did not include the "d3dcompiler_42.dll" in my newest game, but I did have it in the older one, and that would not have been the cause of this problem.
I have noticed another thing. So, when my game is published it puts everything into one big folder.
However, since I had a folder structure in my work folder, I always thought it would make sense to preserve that in the published version. I would manually create the folders in the published version and put all the relevant files in there. So far it has worked with no problems, but I am wondering maybe that could be the cause of this issue?