I don't remember how it worked in LR 2.3 as that is many years ago but the typical way you do this in Lightroom is to make a collection of your images. Set the sort order to custom and drag the images around in the order you want. Than go to slideshow from this collection and they should be in the right order.
Many thanks and let me try.
The current version 6.8 / CC2015.8 also allows me to drag-and-drop photos to different positions on the lower filmstrip under the Slideshow window.
(Hint: Usual advice for "drag-and-drop photos" is to click the cursor on the image- not the border- before you drag.)
Unfortunately my version does not give me an option of Custom short or allows me move pictures from its place. Thanks for trying.
Did you note carefully in the advice from Jao above- "make a collection of your images"
This is the important step. A custom sort order is not possible if you are viewing "All Photographs" or a folder that has sub-folders and the option "Show Photos in Sub-folders" is set to 'on'.
This quote is from the Lightroom-2 help file-
"Rearrange thumbnail images in the Filmstrip and Grid view
❖Select a collection or a folder that does not contain any subfolders, and then drag a thumbnail to a new location."
Page 139 Lightroom Help pdf (3rd Sep 2009)
"Rearrange slide order
If the source for your slide show is a collection or a folder that does not contain subfolders, you can manually rearrange
the slide order.
❖In the Slideshow module, drag photos in the Filmstrip to rearrange them."