This problem has happened to quite a few users, including me. I've had it happen with several versions of MC, on several flavors of Windows.
The problem (if I am on the right track in the first place) is that the self-extracting package extracts its contents, but does not launch the actual setup executable after doing so. This is probably due to a bug in the packager. Here is my proposed workaround (note that a "workaround" is a different thing than a "solution"):
1) Download the file to a known directory (that is, click the download link and select "Save" rather than "Open").
2) Open an Explorer window and double click the downloaded EXE file. You will get a "Media Center setup" dialog, with a progress bar. This dialog will just disappear without launching the setup file... don't worry.
3) Click Start, then Run, type "cmd" (without quotes) in the Open box, and click OK. A command prompt window will open.
4) Type this command in the command prompt window:
echo %temp%
Hit Enter after typing the command. This command will simply tell you what your Windows temp directory is. It will likely spit out the following:
C:\WINDOWS\Temp
-or-
C:\Documents and Settings\[your user name]\Local Settings\Temp
5) Open an Explorer window, and navigate the the directory that was spit out in step (4) above ("C:\WINDOWS\Temp" or whatever). There should be a subdirectory there named something like "RarSFX0". Open that subdirectory.
6) You should see a file named "InstallWizard.exe". Run this file to launch Media Center setup.
Of course, instead of doing steps (4) and (5), you could simply search the Windows drive for the "InstallWizard.exe" file. Whatever works for you.
I hope that helps. It has worked for me every time this problem cropped up.