can you please clarify a few points?
Aperture settings has previews enabled.
Have you enabled "New projects automatically share Previews"?
How is "Share Preview with iLife set"?
I have manually deleted previews and thumbnails from within the aperture library to force a rebuilt.
Has the rebuild worked? Have you checked in the "Masters" folder, if the previews actually exist for the images, that will not be dragged?
Have you checked each project in question, of the Previews for that project are enabled?
Select each of the the projects in question and ctrl-click (right-click) the gear-icon in the upper right corner of the Library inspector. Check the setting for "Maintain previews for project".
If the previews are disabled in that menu, you cannot drag previews from the library.