You should be able to do this while the VM is running. Try connecting it to all three and see if anything changes. One private, one internal, and one external. Now, to find the cause of the problem, I would make 3 networks in the Virtual Switch Manager. In most cases, if the VM guest shows that the Ethernet cable is disconnected, it means that in the settings for the VM the Network Adapter's virtual switch is set to 'Not connected.' Obviously this doesn't seem to be the case for you, but double check to be safe.
