VirtualBox Ubuntu can not connect to internet
It looks like you have not set up the DNS service on your Ubuntu guest. The following commands should take care of that.
sudo su
echo "nameserver 8.8.4.4" >> /etc/resolv.conf
echo "nameserver 8.8.8.8" >> /etc/resolv.conf
exit
Use NAT mode instead of Bridged Mode, make sure your connection works, if it does, then there's something wrong with the Network settings you used in Bridged mode, if it doesn't it's probably your network card, router, or something else.