Finally figured it out. At least at home, and since I’m having the same problem at work, I really think it’s the same problem.
Apparently, during the install process, you need to have it install SQL Server 2005 Express. I, most likely, didn’t install it or it didn’t install because I had the developer edition of SQL Server 2005 installed on my machine and thought that they are equivalent. They are not. When I went back into the Visual Studio 2008 installation and added the SQL Server 2005 Express, the next step added quite a few tools, etc., that had to deal with the SQL Server Compact Edition. When I went back into Studio, the problems that I had been having seem to have disappeared.
I feel like such a moron.