I finally figured it out.

I had to go into the Project Properties pages again. Select Publish from the menu on the left. Then click on the Application Files button and set the Microsoft.VisualBasic.PowerPacks.Vs.dll to Include then go into the Prerequisites and select the option to Download Prerequisites from the same place as my application.

Now when you publish the app it will create a folder for each of the Prerequisites. This will have to be installed manually from these folders on the target PC.

One caveat that I found is that one of the Prerequisites was .Net 3.5 SP 1. When I published it the first time after these changes the build failed because it could not find the .Net file even though I had included the full install package and added it as Include in the Application files area. Once I removed the check for .Net 3.5 SP 1 in the Prerequisites I was then able to publish the app and it did install on the target PC which already had .Net 3.5 installed. That may mean that I will have to manually install .Net 3.5 on any other PCs instead of it prompting to download it during the setup.

Thanks,
Ty