Hello,
According to you discription, if the activation does not happens using the KEY but instead happens (apparently) contacting internal license server while connected on the corporate net, maybe you are using your orgenization's activation license, not a retail key.
Maybe you are connecting to the KMS host server of your corporate, or your corporate uses Active directry based activation. Both kind of activation are volume license activation, so regarding your first question, maybe it cannot use the license key of 'old' on new (transfer), because if you are using a client activation key, it need to be directly installed on a new machine according to the system version.
The suggsestion is to contact your corporate's administrator to help connet your new computer to corporate and verify what type of activation it is, then maybe install a specific windows client activation key and use the host to do activation, it depends on the different activation type.