Also, the computer on which the upload button doesn't work has Silverlight 5.1. This machine it defaulting to Flash. I have another machine with Silverlight 4.1, which defaults to Silverlight, and the button works fine.
I don't know if it's a problem with Silverlight 5.1, but I can't tell my clients to downgrade their version of Silverlight. So I'd like to get Flash or Silverlight 5.1 working.