The latest Firefox still works on Mavericks as of today, and I could hook you up with a clean Mavericks image (straight from my MBP's recovery partition) if necessary.
If I recall correctly, the Mavericks installer required the user / pass of the Apple ID that downloaded that particular installer. Otherwise it wouldn't install.
@MacFoxG4 Mountain Lion can still be bought from Apple here:
Certified Refurbished Products
We test and certify all Apple refurbished products and include a one-year warranty.
www.apple.com
Waterfox still supports Mountain Lion. You could also try lowering the minimum OS version from 10.9.0 to 10.8.0 in the latest Firefox's plist file. See what happens.