I have tried all of the different things I have read here in the forum, but I cannot get this game to run. I am using Windows 7 Pro 64.
I have done elevated mode, all of the different compatibility settings, and installed Quicktime. Nothing works. The game will not start at all. If I set it to 256 colors or 640 resolution, the process will open (and it will change my screen), but the game will never load.
Is there anything else that can be done about this? I know it's old and inexpensive, but I don't want to pay for a game I can't play.

I have exactly the same problem. None of the fixes I found on the web have worked.
ScummVM is working on supporting the game but they are not yet finished. I can run Myst by using the ScummVM daily build, but all of the video sequences are missing right now.

You didn't say which version you have, but the following should work for realMyst on Win7 64-bit.

First, run "C:\Program Files (x86)\GOG.com\realMyst\realMYSTSetup.exe". Make you sure the Myst Setup screen isn't hidden and waiting for your input.

I launch realMyst using the "C:\Program Files (x86)\GOG.com\realMyst\realMystStart.exe" GOGREALMYST" shortcut set to Windows XP SP3 compatibility mode.

Good luck!

Thank you, phatwebs, but sadly I have the Masterpiece Edition and not realMyst :(