As far as I know, I use VirtualBox on Arch and it is automatically connected. Infact, I have to set it to not connect.
In Windows, not exactly sure but you may want to look at some settings.
First, try in VirtualBox. Select the machine you want to connect.Goto its settings then look for Network tab. See what settings you have ticked.
Try starting the VM and in your VM window look for the Network icon (should look something like two computer monitors) and see if it shows 'connected' on an interface. Maybe something like: Adapter 1 NAT: cable connected
Also, you could try going to Windows Network Connections in the Control Panel.Look at what adapters you have. You SHOULD have atleast one virtual adapter which connects to your network card adapter.You may need to adjust LAN settings if VirtualBox is showing you are connected but you aren't actually establishing a connection from the VM.
Can't really say at this point because I'm not on Windows at the moment. Nor do I use VirtualBox on Windows. But it might give you some ideas where to look for problems.