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How do I operate the laptop via the docking station and keeping the laptop shut?
What model Vaio do you have?
Which docking station?
What Operating System are you using?
What happens when you shut the lid? Does it go into Sleep Mode? If so you need to change the Power Management Options for closing the lid from "Sleep" to "Do Nothing". If you are using Vista or Windows 7 you can do this for all Power Plans or for individual Power Plans - see this link for instructions for either of these: -