Colorbox not working in new content type
This problem might occur because the path to library is incorrectly set. It is typically like so:

libraries\colorbox\jquery.colorbox-min.js


Though via /admin/config/media/colorbox it is possible to set some other path for it (within 'advanced settings').

There was a time (some older version in colorbox) that the solution was to correct the path to the Colorbox plugin directory, so that after unpacking it looked like so:

sites/all/libraries/colorbox/colorbox/jquery.colorbox-min.js


Refer to issue #1906156 for more details on this.

If that doesn't help, then check if there are any other modules that use Colorbox that are trying to find it on this path.

Of course, make sure also that the "permissions" to the plugin are set correctly (if no read access is granted, then that is probably what is causing the problem).