Do you mean this information page?

If so, when I opened the page from your link, then clicked on the "Download now" link, the browser changed to the page above, then the download option window appeared and I downloaded the software to my Desktop. If that page is different for you, please let us have that link.

Do you have any add-ons, either in Firefox or IE? If so, anything there that looks strange?

In Firefox, Contents tab, is Javascript enabled? In the Privacy tab, select "Use custom settings for history" from the "Remember history" button. Are 2rd party cookies accepted?

What happens if you try both Firefox and IE in their Safe Modes? To run Firefox in Safe Mode in XP goto Start > Run, type in
firefox -safe-mode and click OK. (Spaces are important, so copy/paste if you wish).

To run IE8 in it's Safe Mode, goto Start > All programs > Accessories > System Tools then "Internet Explorer (No Add-ons)". That entry may be under Accessories and not the System Tools sub-folder.

Any other security applications running, eg Spybot Search & destroy, Spywareblaster, etc?

When did this stop working, and what has changed since then?