I just bought and installed Myst Masterpiece Edition, but unfortunately I can't get it to run. When I attempt to launch it, my screen goes black for about three seconds and then it crashes, with this description of the error:
AppName: myst.exe AppVer: 0.0.0.0 ModName: quicktime.qts
ModVer: 6.3.0.17 Offset: 00237a8c
I'm running 32-bit Windows XP. I'm using an ATI graphics card with fully updated drivers, and I've fooled around with the compatibility mode to no avail.

Similar problem here. I'm running on 64 bit vista and when I don't do compatibility mode, the quicktime videos don't play, and when I do compatability mode, it doesn't play. I have to Ctrl+Alt+Del out

Remove the Quicktime and try again.
If you still want to use Quicktime you can reinstall it or install Quickitime Alternative instead.