I understand that you installed it ok, but did you run the installer with the Run as Administrator option? It does make a difference. You don't need to run Zimbra Desktop itself with that option. You could also try turning off UAC before running the installation and see if that makes a difference.
Lastly, do you know if that
VB Script "zdrun.vbs" exists on your computer? Can you run it manually? If not, then you probably need to enable the Microsoft scripting engine. See this link for instructions:
How to Enable Windows Script Host | eHow.com.
It's also possible that there is something corrupted in the scripting engine itself. A repair of Vista or a System Restore may rectify that. It could also be that the Path Environment variable doesn't include the C:\Windows\System32 folder which is where the cscript executable is located, which is what runs vbs files.