I see,
what you describe sounds like a problem with the resolution of the game. It probably defaults the resolution of the game to something unsupported by your monitor. We need to somehow force it to run in a proper resolution.
You could try finding the options file of the game and editing it manually. The default location where the options.txt file is located should be
C:\Documents and Settings\[YOUR USERNAME]\Application Data\Atari\RCT3
You might need to have Viewing Show Hidden Files, Folders and Drives enabled in your windows explorer. If you find the options.txt file then open it for editing with notepad and check for the line Resolution xxxx xxxx and change it to your monitors native resolution - e.g. 1920 1080. Then save...