on your Windows PC open QuickTime Player. Click edit > settings > quicktime settings. In the appearing window click the last tab and select safe mode (gdi only) in the video section.
hmmm… maybe another video capable application has grabbed the .mov extension on this particular pc or the QT browser extension is disabled in the browser itself. You can check this out at the standard applications pref pane (hope this is the right name, I only have a german xp here) and in the browsers plugin settings.