Install update #3 and replace this file with the original RCT3plus.exe 
in the installation folder.This will make the game NOT ask for the CD.

Tested and working!!!!

Just a comment of my own.I had the LAST driver of my Nvidia card installed and it WOULD NOT RUN!
I uninstalled the new drivers and installed my old ones and it WORKED.So this is a hint for those that have a GeForce card.