Regarding Vista usage --
In my case, I have Vista 64-bit installed, and UAC turned on, but with less elevation prompts: http://www.howtogeek.com/howto/windows-vista/disable-user-account-controluac-for-administrators-only/
This worked fine to install Tropico normally, and Paradise Island as well. I didn't bother installing DirectX 7.0a, I had the DX9 redist already installed: http://www.microsoft.com/en-us/download/details.aspx?id=8109
I needed to use "Run As Administrator" to install the patches.
I find I can crash Tropico if I'm too liberal with use of the editor; something about the game seems to not always like being edited a lot.
So if anyone reading this has had difficulty, try the above, especially as UAC is kind of annoying on Vista anyway. I don't know how applicable this is to Win7, but you can give it a try.