You would have to install that package from the RedHat repository. Best to ask about that in RedHat support.

Have you considered installing a newer distro that has the modern libraries and packages that the newer versions of Firefox require? Red Hat Enterprise Linux WS release 4 is from 2006-03-07 - it is almost 5 years old. You might need more than one updated package, those error / warning messages appear serially - fix one and then the next one appears, and you may have that happen repeatedly.

Upgrading the whole OS is not a viable option in this situation (long story).

Maybe it would work to go the other direction: what's the most recent Firefox that will run on this system without getting into dependency hell?

My guess is that Firefox 2.0.0.x versions would probably be the latest that would work. See if your version of RedHat meets Firefox 2.0 system requirements:
http://www.mozilla.com/en-US/firefox/system-requirements-v2.html

Firefox 3.0 had many changes that rendered older versions of most operating systems as being no longer compatible. I am far from an expert with Linux (more like a real noob), but I did a lot of research for updating my EeePC a few years ago, and it seems like most Linux distros from 2006 thru like mid-2008 just didn't have the necessary libraries or packages for Firefox 3.0+ versions. I currently have a custom Netbook distro called Easy Peasy installed, which was made from Ubuntu 10.04 .

Win98/SE/ME and MacOSX 10.3.9, along with most mid-2008 and older Linux distros just don't work with Firefox 3.0 thru 3.6 versions. The same thing is happening with Firefox 4.0 dropping compatibility for some OS's - on MacOSX support for the PPC hardware is gone, and W2K & WinXP SP1/2 isn't blocked, but it isn't supported either.

Worth a try, if I can find the download somewhere. The download links on that page take me to the 3.6.13 download :(

Sorry I didn't think of giving you the FTP folder for downloading 2.0.0.20.
ftp://ftp.mozilla.org/pub/firefox/releases/2.0.0.20/linux-i686/en-US/

Found it! Old releases are under http://releases.mozilla.org/pub/mozilla.org/firefox/releases

Looks like we posted at almost the same time :)

2.0.0.20 does run on this system. That will solve the problem until I can get an OS upgrade (already in the pipe, but at least a few weeks away).