Why does the "choose files" button not work in Wordpress 2.5 when trying to upload photos?

Programmer Question

I've got Wordpress 2.5 installed on my website. It works well, but I can't get the photo uploader to work. When I'm writing a post, I click on the "Add media" button. In the "Choose File" tab, I see the "Choose files to upload" button. When I click on it, nothing happens. I searched the net and found nothing helpful. One page vaguely mentioned having the latest Flash player. I verified and confirmed that I have the latest player. Any ideas?

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