The official Android-X86 builds do not have Ethernet support, so you won't have an Internet connection while running Android-X86 in VirtualBox. You can, however, use a custom Android-X86 4.0.4 RC2 build that adds Ethernet support: DOWNLOAD (thanks to Ron M for this build!).
Important: if the mouse isn't working, select from the VirtualBox menu: Machine > Disable Mouse Integration.
This build has the ARM translator libraries build-in. This is a debug build so a red frame is displayed sometimes - the only way to avoid this is to compile Android-X86 from sourceand apply the Ethernet patch yourself (or search for a different Android-X86 4.0.4 RC2 ISO with Ethernet patch).