The plot thickens. I hadn't thought about the buttons being drop down menus instead of links, which would explain why they didn't behave like links. On my computer, the buttons do not work at all with FF but do work with IE. However, IE blocked the embedded links and gave me the option to unblock it. Don't know if the behavior is different today than when I looked before or whether I previously just stopped looking when FF did not work at all and the buttons did not behave like links in IE.
There is nothing wrong with your computer. If there was, you would be having trouble with most web sites. This web site is just not well-behaved. It appears that the programming for this web site is extremely particular about the browsers and settings it will interact with. I'm not sure why IE blocked the web site's links, but the same characteristics may be causing problems with other browsers, as well. It is also possible that add-ons in your browsers are preventing your browsers from handling the site properly. Another possibility is that the site, itself, is refusing to function because it wants to do something as a condition of your using the web page that is being blocked, like loading cookies or funneling user information to a third party. You could try opening your browsers in "clean" mode (all add-ons suppressed) and see if you have more luck, but you may be having problems for a reason (you are being protected from something that is set to be rejected by default).