I admit to knowing nothing about Macs but the first thing I'd be trying to check is is it connected to the network at all. Do other internet programs work, things like e-mail clients or other browsers?

If you don't have any such things installed go to Applications > Utilities > Terminal and type ping 8.8.8.8. That will 'ping' Googles DNS server as a test. If that works then it MAY be a Firefox specific problem. If not it's the computer or OS.

See below for what good and bad results look like.

To thepillenwerfer. Thank you very much for replying with the suggestion of what to do. I shall keep the reply for the future, After no internet overnight, the connection came back two hours ago with no indication as to why. This has happened before and I put it down to a problem of reception in south east London, England. The tests you have suggested will narrow down what is wrong when the internet fails again. Good wishes.