Thanks for your feedback, it's helpful. I finally checked my version of Firefox and updated from v12 to v25.0.1 (!!) (I don't use it very often!). And as part of that got a bunch of Java warnings and updated from whatever version I had to the latest, and uninstalled 3 old versions.
The shiptrak map now working in Firefox, pretty much as normal. But in spite up fooling around with Chrome, no joy at all with Chrome (even after an update, reboot, clearing cache, etc etc). IE 8 also doesn't work.
I also went to my sister's nearly brand new Dell computer running Win 7, and tried calling up shiptrak.org on IE 10. Still no joy.
But since I finally got the Shiptrak page up on Firefox, I got the contact email and I have emailed that person with a screen shot and details of my issues. I'll post back here if/when I hear back from them.
Thanks for your help!