I've figured out the problem and solution, and thought I'd post it here in case anyone else is having the same problem.
It appears the Shockwave Flash Object Add-on was disabled for some reason.
To fix it, I opened IE, went to Tools> Manage Add-ons and enabled it.
Now everything seems to be working fine
Just a suggestion, you may want to have that solution page updated to refer to IE 8 as well, for others encountering the problem.
I searched but never saw that solution when I was searching the site for help, because the problem was occuring with IE 8 instead of IE 9, so I was skipping over IE 9 specific solutions.
I agree. I'll have to tweek some of the instructions a bit but it would be better if it referred to both IE 8 and 9.