JPEG Images Being Copied to Root with Garbled File Names on IIS7 Web Server

What is happening is that whenever our website tries to load a JPEG file from a non-local source (another website for instance), it appears fine in the raw html but when the page is displayed in a web browser the file name changes from 'http://www.website.com/image.jpg' to '/0ac5dd22599c9a2e9ced06e1aaee901f.jpg'.  The file name is always different, but is always a long string of characters like that.  It loses whatever web address it had and appears like that.  At the same time it creates a copy of the image of the root directory of the server drive (C:\) with the same file name.  Of course since the website proper only sees what is in its folder (C:\inetpub\wwwroot\) it can't see any of those files and just displays a broken image.

So what we know is:
- We are using IIS 7 for the web server.
- It only affects JPEGs.
- It only appears to affect non-local sources. Locally hosted JPEGs inside the wwwroot folder display fine.
- The same JPEGs work fine when tested on another web server.
- The other web server is a clone of the affected one, yet performs normally.

We are about to toss this one in the pile of Great Mysteries along with 'Bigfoot' and 'Why People Liked Achey Breaky Heart', so any and all ideas are welcome and we thank you in advance.