I would have tried your suggestion, Fou-Lu, but it is no longer necessary. I had read someone's suggestion in another forum to install and run the Revo Uninstaller, and use it to completely remove any and all traces of Java. I did so, and then the Java 7 offline install worked, flawlessly.
Thanks for your help.
If anyone knows of a website that can offer ColdFusion help that isn't controlled by neurotic, pedantic jerks* (stackoverflow.com), please PM me with a link.
* The neurotic, pedantic jerks are not the owners; just the people who are in control of the "popularity contest".