I am looking for free software (trial software is fine) which will
count the number of images within one jpg file.  This will make much
more sense if you look at the jpg image which can be found at
http://images.andale.com/f2/102/106/11653747/photoalbum/1056711454421_Flash0190.jpg

This should count as 7 images.  The software needs to be able to scan
through all JPGs that may be nested under multiple directories and add
all of the images up under all JPG files.

I have worked as a professional computer graphics artist, and I doubt
that such software exists for free. It may not exist at any reasonable
price.

For a human being to analyze this sort of composite image seems
relatively simple, but creating software that can do so accurately is
very difficult indeed. High-level pattern recognition software has
been developed, but the commercial market for the kind of thing you
want would be small, and I doubt that you will find a suitable program
that functions as you describe.