Cannot install SQL Server Express 2008, 2008 R2, or 2012 on Win7 Pro x64

I have a Dell Vostro 3750 with an Intel Core i3 and 8GB RAM running Windows 7 Professional 64-bit.
I'm trying to install SQL Server Express and cannot get ANY of the installers to work.  I have tried every version of the installers (both x86 and x64) for 2008, 2008 R2, and 2012 and they all do the same thing:
The installer will unpack the files, then immediately after the files are unpacked a Command Line or Powershell window will open for a split second and disappear.  Nothing will get installed, and no error message ever comes up.  The event logs show nothing.
Any idea what is going on here?  I have never had any trouble installing any other software.  I am running Office 2010, Visual Studio 2008, Visual Studio 2010, Visual Web Developer 2010 Express, and Visual Studio 2012 Express with no issues.  I believe SQL Server 2008 Express may have been installed successfully and uninstalled 2 years ago, but it's not ther ...