It's weird, because I also run Matriux on VirtualBox, but all browsers work fine. As well as the connection.
May be it doesn't really matter, but, do you run wired or wireless connection ?
Did you ping actually the websites you wanted to visit ?
Check out ifconfig if there's everything alright, and then also /var/log for some changes in logs, may be the were some errors logged. That might help diagnose the problem.
Also, you can check if browsers work, when booting from the Live CD actually, although I don't know how it can help, still it's something.
