If someone with Java 1.3 or 1.4 installed on their computer could please download the Windows free trial from the Bingo Card Creator site, install it, and tell me whether you get to the main screen or not, I would be obliged.
I believe the problem was that earlier I had assumed, having set the compiler to use version 1.3 in Eclipse, that I was getting Java 1.3 class files. That worked for a long, long time. Then I made an ant script and, boom, it stopped working the first time I ran the clear target and Ant used the (defaults to 1.6) javac target to make the new build. Of course, having 1.6 on this machine, I never noticed the change.
All I can say is doh!