[Quick Edit - Lance, I have exactly the same situation. Frustrating.]
Here's an update from me. The game didn't run after my initial post, and I gave up for a bit. After reading the new posts above, I decided to try again. I've now had the game running and on the main menu twice, but it's still a poop-show by the looks of it.
First, I switched my default audio from a Turtle Beach Stealth 450 headset, back to my internal SB Z. I did this right after booting, I didn't actually disable or remove the audio device or wifi dongle - and Myst IV started properly, main menu and music playing. I then decided - because I'm a programmer and don't know any better - to test it failing again. Switched back to the headset default, sure enough the game doesn't start. Switch back to the SB Z... game still doesn't start. Fantastic :)
So, I rebooted with SB Z set to default, tried again - Myst IV started. Closed the game, fired straight back up with no changes - it won't start. So, on top of some kind of disagreement with audio devices and/or peripherals that's killing the game on initial launch, we also seem to have a problem launching the game a second time with no changes made to the system. The process isn't hanging around after it kicks back to desktop and preventing GOG from launching it either - it's definitely gone from the process list afterwards.
Here's the real kicker though. I now can't start it at all - even after rebooting, and even while my SB Z is the default audio device. I can't find any consistency with this - I could have played the game twice this morning if I wasn't testing to find a cause, and now I'm unable to play again and still have no explanation for any of this :)
Thanks for posting your updates guys, and good luck getting any further. I can only stand so many reboots before I'm burned out and giving up!