Firefox recognizes and "enables," but doesn't use, local Java

This issue has been posted about a few times before, and, if my search-fu is to be trusted, has never been resolved, or even replied to. Here's hoping for a break from tradition.

First, I want to state clearly, and for the record, that this is not a request for portable Java. I don't need portable Java and I don't care about portable Java.

I recently started using portable Firefox at work, because I prefer it over Internet Explorer and I use my browser quite a bit during the workday. However, I've run into an interesting problem. The machine (Window Vista) has Java 6 installed, and IE recognizes and successfully uses it for running embedded Java apps, but, while Firefox, in about:plugins, claims to recognize Java (and marks it as "enabled"), Java apps run in Firefox do not load at all. A trip here in IE says my Java is working, listed as "Java 6 update 0," but in Firefox I get only a blank box.

Anybody have any idea what's happening?