If NAT doesn't work (doesn't surprise me) and you can't use Bridged mode, create a Host-only network. A Host-only network behaves like a Bridged network, but there is no connection to the physical network. Essentially it creates a virtual switch and connects the virtual adapters to that. If you need an adapter on the host system, a Microsoft Loopback Adapter will likely work if VirtualBox doesn't supply virtual host adapters.
If you need to get to the Internet from the guest as well, create an additional network adapter in the guest which uses NAT.
Be sure not to create any virtual or physical networks on the same IP subnet. They are separate networks and must be configured with different IP subnets or your computer will send data packets to the wrong location! Your communication will silently fail, as you will have essentially told your computer to turn left when it needed to bear right.
This is trivial to configure on VMWare Workstation with the Virtual Network Editor. I haven't used VirtualBox since v2, but I can see from the manual that this type of configuration is possible.