I used Time Machine to transfer all the files across. And I thought I'd checked it all out. Clearly I hadn't checked this! And sadly, the old machine has now gone. And so have all the back-up files too - since I thought everything was OK. I only discovered this today and now wish I had the old library back!
In fact I've been looking at this over the last few minutes and sadly there are around a dozen or more slideshows that have simply disappeared.
My fear now is that if I go to the trouble of making more slideshows what will happen to them when I upgrade in the future?
Apply the two fixes below in order as needed:
Launch iPhoto with the Command+Option keys held down and rebuild the library.
Since only one option can be run at a time start with Option #3, followed by #4 and then #1 as needed.
Using iPhoto Library Manager to Rebuild Your iPhoto Library
1 - download iPhoto Library Manager and launch.
2 - click on the Add Library button, navigate to your Home/Pictures folder and select your iPhoto Library folder.
3 - Now that the library is listed in the left hand pane of iPLM, click on your library and go to the File ➙ Rebuild Library menu option.
4 - In the next window name the new library and select the location you want it to be placed.
5 - Click on the Create button.
Note: This creates a new library based on the LIbraryData.xml file in the library and will recover Events, Albums, keywords, titles and comments. However, books, calendars, cards and slideshows will be lost. The original library will be left untouched for further attempts at fixing the problem or in case the rebuilt library is not satisfactory.