I've got to get this out of the way first:
You really, really need to turn off that system. Security updates haven't been released for it for over five years — and, what's more, that release is from back in the dark ages when the project hadn't really gotten off the ground.
If you must keep it similar, moving to CentOS 5 will give you an only slightly updated set of software but with current updates and some lifecycle left to go.
All that said, if I were forced at gunpoint, the thing I'd try is downloading the non-rpm-packaged tarball of Firefox directly from mozilla. It may be that the system is still too old for that, but I think it's your best bet.
Well, fourth best bet, behind upgrading to Fedora 15, upgrading CentOS 5, or just throwing the system in a dumpster.