I had BG working fine. I then tried moving the main gallery directory (required by other changes I was making) and have ended up with BG displaying the thumbnails, but without the necessary markup for the ul or li tags, or adding the Lightbox reference onto the images.

Correct markup (on live site):

<p><ul class="brilliant-gallery" style="font-size:0; margin:0px; dummy: 0; padding:0px; width: 524px;">
<li style="font-size:0; float: left; width: 125px; list-style: none; background: #000000; height: 94px; padding: 3px; text-align: center; margin: 0px; border: none;">
<a href="http://www.letchwortharts.org/sites/all/modules/brilliant_gallery/image.php?imgp=L2hvbWUvc2l0ZXMvbGV0Y2h3b3J0aGFydHMub3JnL3B1YmxpY19odG1sL2xldGFydHMvc2l0ZXMvZGVmYXVsdC9maWxlcy9jb21tb24vZ2FsbGVyaWVzL01vc2FpYyB3b3Jrc2hvcC9BZHVsdCBsZWFybmVycyAxIG1vc2FpYyB3b3Jrc2hvcCBNYXkgMDkuanBn&imgw=1000&imgh=750" rel="lightbox[3880910]"><img style="border: 0; margin:0px; padding:0px;" alt="" src="http://www.letchwortharts.org/sites/all/modules/brilliant_gallery/image.php?imgp=L2hvbWUvc2l0ZXMvbGV0Y2h3b3J0aGFydHMub3JnL3B1YmxpY19odG1sL2xldGFydHMvc2l0ZXMvZGVmYXVsdC9maWxlcy9jb21tb24vZ2FsbGVyaWVzL01vc2FpYyB3b3Jrc2hvcC9BZHVsdCBsZWFybmVycyAxIG1vc2FpYyB3b3Jrc2hvcCBNYXkgMDkuanBn&imgw=125&imgh=94&imgcrop=1" /></a>
</li>
...

Incorrect code (on test site after changes):

<p><ul><li>
<a href="http://test.letchwortharts.org/sites/all/modules/brilliant_gallery/image.php?imgp=L2hvbWUvc2l0ZXMvbGV0Y2h3b3J0aGFydHMub3JnL3B1YmxpY19odG1sL3Rlc3Qvc2l0ZXMvZGVmYXVsdC9maWxlcy93ZWJmbS9jb21tb24vZ2FsbGVyaWVzL01vc2FpYyB3b3Jrc2hvcC9BZHVsdCBsZWFybmVycyAxIG1vc2FpYyB3b3Jrc2hvcCBNYXkgMDkuanBn&amp;imgw=1000&amp;imgh=750"><img alt="" src="http://test.letchwortharts.org/sites/all/modules/brilliant_gallery/image.php?imgp=L2hvbWUvc2l0ZXMvbGV0Y2h3b3J0aGFydHMub3JnL3B1YmxpY19odG1sL3Rlc3Qvc2l0ZXMvZGVmYXVsdC9maWxlcy93ZWJmbS9jb21tb24vZ2FsbGVyaWVzL01vc2FpYyB3b3Jrc2hvcC9BZHVsdCBsZWFybmVycyAxIG1vc2FpYyB3b3Jrc2hvcCBNYXkgMDkuanBn&amp;imgw=150&amp;imgh=113&amp;imgcrop=1" /></a>
</li>
...

The result is I see an unordered list of thumbs, with no lightbox.

Somewhere this has got stuck into the database, and I cannot clear it out. I have uninstalled the module, and reinstalled it again, moved the main directory back to where it came from, and cleared all caches I can find, with no effect.

Can you (a) identify how to restore correct working, and (b) fix the problem?

With thanks,
Tony.