This particular problem of Firefox starting in Offline Mode is particularly because of a network unavailability problem. And is common when you have your NetworkManager turned on along with the network service. The best possible workaround for this problem is you disable the NetworkManager service as this will also get you off from some other similar network problems such as Pidgin not logging in and staying on a status message mode - 'Waiting for Network Connection' and other Network consuming programs such as Lifrea - too starting in offline mode. You can disble NetworkManager service from starting by issuing the following commands in a terminal as root:

If you want NetworkManager to keep running then you could try this fix for Firefox instead, but then you won`t be able to get your Lifere and Pidgin programs running correctly!

1) Goto the about:config property editor of Firefox by typing the about:config and click on the next message that says something like "careful.....promise.....".

2) In the filter, search for toolkit.networkmanager.disable and set it`s value to true and restart your Firefox browser, You`re done!