Aug 22, 2013 I stopped being able to update Firefox probably around 2 years ago on my computer, and can't download Google Chrome, all because I am running 10.4.11. I don't need to do so much on my computer.I browse the web, talk to people on skype, listen to music, watch movies, and type things up. Download Mozilla Firefox for Mac, a free Web browser. Firefox is created by a global non-profit dedicated to putting individuals in control online. Get Firefox for Mac today!
You need some more RAM, but:
Start by checking if you can run Snow Leopard:
Firefox For Mac Os 10.8.5
Requirements for OS X 10.6 'Snow Leopard'
OS 10.6 Snow Leopard is once again available from the Apple Store:
and in the UK:
but nobody knows for how long it will be available.
To use iCloud you have to upgrade all the way to Mountain Lion:

You can also purchase the code to use to download Lion (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.
Mozilla Firefox is a graphical web browser developed by the Mozilla Corporation and a large community of external contributors. Firefox started as a fork of the Navigator browser component of the Mozilla Application Suite. Firefox has replaced the Mozilla Suite as the flagship product of the Mozilla project, under the direction of the Mozilla Foundation.
To display web pages, Firefox uses the Gecko layout engine, which implements most current web standards in addition to several features which are intended to anticipate likely additions to the standards. Latest Firefox features include tabbed browsing, spell checking, incremental find, live bookmarking, a download manager, private browsing, location-aware browsing (also known as 'geolocation') based exclusively on a Google service and an integrated search system that uses Google by default in most localizations. Functions can be added through add-ons, created by third-party developers, of which there is a wide selection, a feature that has attracted many of Firefox's users. Mozilla Firefox is a cross-platform browser, providing support for various versions of Microsoft Windows, Mac OS X, and Linux.
Firefox Features
- Improved Tabbed Browsing
- Spell Checking
- Search Suggestions
- Session Restore
- Web Feeds (RSS)
- Live Titles
- Pop-up Blocker