Welcome to askubuntu, and congratulations for diving into a decent computing environnment.
I suspect your wireless is connected, but you may have a DNS problem.
Try these 2 simple ping commands, in a console:
If the second ping does not resolve ( it should return 3 ping results by default), this would mean you HAVE an Internet connection, just no properly configured DNS resolver.
If that is the case, I suggest you configure your DNS by following this guide.
Oh, if you need a DNS server to setup against you can use google's public dns service.
If both pings do not resolve, it could be you are connected to your router but the router is not connected to Internet.
If you want to rule out that firefox is the culprit, try installing chrome or even lynx:
sudo apt-get install lynx
sudo apt-get install chrome
Then, in a console:
If this brings you the beautiful google page (in text mode), Firefox is the culprit. I would surprised if this was the case. I am betting you have a (quite common) DNS configuration problem.
Hope that helps. Cheers!