I added the line class="thickbox" to the url of the imageslinks. In the statusbar I can see that the link is ok. The overlay screen is loaded, but the actual image is not displayed.
So I changed the links in the of the album.php to point to the thickbox files I'm using within my WordPress installation. Tried again and I could see that the link was diverted to my WP thikcbox files because in the css of those files I deleted the overlay screen. But still the images don't show up in ZP while it works ok inside WP.

Anyone with experience of using Thickbox within ZP? Perhaps there is a conflict in code/javascript I'm not aware about?

I've experienced this once with my Plogger installation. Then it was a line 'deny all' which was somehow included into the .htaccess file in the /images folder. But this is not the case here.

EDIT: Just tried it with Lightbox. Same thing: lightbox starts up, overlay screen, white box, but no images loaded. When I disable lightbox or thickbox I get redirected to the standard one-image-per-page screen of my theme.

Actually that should work, thickbox is actually already included within zp.core/js and is used by default theme to show the exif data on image.php.

Check you options in the admin how the image protection is set, too.

Well, I just added thickbox to the of the default theme and added class="thickbox" to the imagelink. The overlay screen appears again, but no images... The admin toolbox and exif data is presented as should.

The 'Full image protection' is set to 'unprotected'.

Ok, I tried it out, the image protection must be the following "unprotected" and "disable hotlinking" must be unchecked, since the full size image is called.

My settings were exactly what you describe, but no images...

But I found the 'error' ...
I had to change getImageLinkURL into getFullImageURL in album.php. That was all...
It came to me when after disabling mod_rewrite the thickbox window appeared with the complete webpage in it and not just the image

I know this is an old post but I had a similar issue, setting it to unprotected did fix it - doh would be nice if the protected worked as well - ah well...

This is a limitation in the Thickbox js. You could try to use the iFrame function of the Thickbox for example if you really need this and make a extra theme page to call the full image or a special bigger resized one.